{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Light FM Approximate Nearest Neighbours (ANN) example\n",
    "\n",
    "In this notebook, we'll be building a hybrid LightFM model on the example movielens dataset. \n",
    "\n",
    "We'll then store the item and user vectors, and build an ANN index over these for fast querying at scale. This technique can produce < 50ms response-times across millions of items.\n",
    "\n",
    "We'll look at two popular ANN libraries, Annoy and NMSlib, and compare their performance.\n",
    "\n",
    "Dependencies:\n",
    "- Annoy - https://github.com/spotify/annoy\n",
    "- NMSLIB - https://github.com/searchivarius/nmslib/tree/master/python_bindings\n",
    "\n",
    "Firstly, let's import the data and build the Light FM model, as per the example in the docs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lester/anaconda2/lib/python2.7/site-packages/lightfm/_lightfm_fast.py:9: UserWarning: LightFM was compiled without OpenMP support. Only a single thread will be used.\n",
      "  warnings.warn('LightFM was compiled without OpenMP support. '\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.metrics import pairwise_distances\n",
    "import time\n",
    "from lightfm.datasets import fetch_movielens\n",
    "\n",
    "movielens = fetch_movielens()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('test', <class 'scipy.sparse.coo.coo_matrix'>, (943, 1682))\n",
      "('item_features', <class 'scipy.sparse.csr.csr_matrix'>, (1682, 1682))\n",
      "('train', <class 'scipy.sparse.coo.coo_matrix'>, (943, 1682))\n",
      "('item_labels', <type 'numpy.ndarray'>, (1682,))\n",
      "('item_feature_labels', <type 'numpy.ndarray'>, (1682,))\n"
     ]
    }
   ],
   "source": [
    "for key, value in movielens.items():\n",
    "    print(key, type(value), value.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train = movielens['train']\n",
    "test = movielens['test']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision: train 0.73, test 0.10.\n",
      "AUC: train 0.97, test 0.91.\n"
     ]
    }
   ],
   "source": [
    "from lightfm import LightFM\n",
    "from lightfm.evaluation import precision_at_k\n",
    "from lightfm.evaluation import auc_score\n",
    "\n",
    "model = LightFM(learning_rate=0.05, loss='warp', no_components=64, item_alpha=0.001)\n",
    "\n",
    "model.fit_partial(train, item_features=movielens['item_features'], epochs=20 )\n",
    "\n",
    "train_precision = precision_at_k(model, train, k=10).mean()\n",
    "test_precision = precision_at_k(model, test, k=10).mean()\n",
    "\n",
    "train_auc = auc_score(model, train).mean()\n",
    "test_auc = auc_score(model, test).mean()\n",
    "\n",
    "print('Precision: train %.2f, test %.2f.' % (train_precision, test_precision))\n",
    "print('AUC: train %.2f, test %.2f.' % (train_auc, test_auc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the item embeddings by simply multiplying the item features by the models item feature embeddings. Even better, LightFM has a performant built-in function to retrieve these embeddings givin a set of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_, item_embeddings = model.get_item_representations(movielens['item_features'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's make an annoy index for item to item querying:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from annoy import AnnoyIndex\n",
    "\n",
    "factors = item_embeddings.shape[1] # Length of item vector that will be indexed\n",
    "annoy_idx = AnnoyIndex(factors)  \n",
    "for i in range(item_embeddings.shape[0]):\n",
    "    v = item_embeddings[i]\n",
    "    annoy_idx.add_item(i, v)\n",
    "\n",
    "annoy_idx.build(10) # 10 trees\n",
    "annoy_idx.save('movielens_item_Annoy_idx.ann')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And query the index for similar movies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nearest_movies_annoy(movie_id, index, n=10, print_output=True):\n",
    "    nn = index.get_nns_by_item(movie_id, 10)\n",
    "    if print_output:\n",
    "        print('Closest to %s : \\n' % movielens['item_labels'][movie_id])\n",
    "    titles = [movielens['item_labels'][i] for i in nn]\n",
    "    if print_output:\n",
    "        print(\"\\n\".join(titles))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closest to Nightmare Before Christmas, The (1993) : \n",
      "\n",
      "Nightmare Before Christmas, The (1993)\n",
      "Beauty and the Beast (1991)\n",
      "Fantasia (1940)\n",
      "Aladdin (1992)\n",
      "Jurassic Park (1993)\n",
      "Sword in the Stone, The (1963)\n",
      "Snow White and the Seven Dwarfs (1937)\n",
      "Lion King, The (1994)\n",
      "Princess Bride, The (1987)\n",
      "Monty Python and the Holy Grail (1974)\n"
     ]
    }
   ],
   "source": [
    "nearest_movies_annoy(90, annoy_idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not bad, and it's very quick:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 5.72 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100000 loops, best of 3: 15.4 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "nearest_movies_annoy(90, annoy_idx, print_output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about NMSlib?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import nmslib\n",
    "\n",
    "# initialize a new nmslib index, using a HNSW index on Cosine Similarity\n",
    "nms_idx = nmslib.init(method='hnsw', space='cosinesimil')\n",
    "nms_idx.addDataPointBatch(item_embeddings)\n",
    "nms_idx.createIndex(print_progress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nearest_movies_nms(movie_id, index, n=10, print_output=True):\n",
    "    nn = index.knnQuery(item_embeddings[movie_id], k=10)\n",
    "    if print_output == True:\n",
    "        print('Closest to %s : \\n' % movielens['item_labels'][movie_id])\n",
    "    titles = [movielens['item_labels'][i] for i in nn[0]]\n",
    "    if print_output == True:\n",
    "        print(\"\\n\".join(titles))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closest to Nightmare Before Christmas, The (1993) : \n",
      "\n",
      "Nightmare Before Christmas, The (1993)\n",
      "Beauty and the Beast (1991)\n",
      "Fantasia (1940)\n",
      "Aladdin (1992)\n",
      "Star Trek: The Wrath of Khan (1982)\n",
      "Heavy Metal (1981)\n",
      "Jurassic Park (1993)\n",
      "Aristocats, The (1970)\n",
      "Blade Runner (1982)\n",
      "Bram Stoker's Dracula (1992)\n"
     ]
    }
   ],
   "source": [
    "nearest_movies_nms(90, nms_idx, n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 4.93 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 26.7 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit \n",
    "nearest_movies_nms(90, nms_idx, n=10, print_output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Again, good and maybe a little better, and also very fast. Now we'll do an example showing how we can do user recommendations using a neat trick outlined by the Xbox recomendations team: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/XboxInnerProduct.pdf . Thanks to Ben Fredrickson https://github.com/benfred/ for bringing this one to light.</p>\n",
    "\n",
    "<p>Basically we add a nomalizing factor to each item vector - making their distances equal with each other. Then when we query with a user vector, we add a 0 to the end, and the result is proportional to the inner producct of the user and item vectors. This is a sneaky way to do an aproximate maximum inner product search."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "norms = np.linalg.norm(item_embeddings, axis=1)\n",
    "max_norm = norms.max()\n",
    "extra_dimension = np.sqrt(max_norm ** 2 - norms ** 2)\n",
    "norm_data = np.append(item_embeddings, extra_dimension.reshape(norms.shape[0], 1), axis=1)\n",
    "\n",
    "#First an Annoy index:\n",
    "\n",
    "user_factors = norm_data.shape[1]\n",
    "annoy_member_idx = AnnoyIndex(user_factors)  # Length of item vector that will be indexed\n",
    "\n",
    "for i in range(norm_data.shape[0]):\n",
    "    v = norm_data[i]\n",
    "    annoy_member_idx.add_item(i, v)\n",
    "    \n",
    "annoy_member_idx.build(10)\n",
    "\n",
    "# Now an NMS index\n",
    "\n",
    "nms_member_idx = nmslib.init(method='hnsw', space='cosinesimil')\n",
    "nms_member_idx.addDataPointBatch(norm_data)\n",
    "nms_member_idx.createIndex(print_progress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define our user vectors\n",
    "\n",
    "_, user_embeddings = model.get_user_representations()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now we can query as per the standard LightFM example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample_recommendation(user_ids, model, data, n_items=10, print_output=True):\n",
    "    n_users, n_items = data['train'].shape\n",
    "\n",
    "    for user_id in user_ids:\n",
    "        known_positives = data['item_labels'][data['train'].tocsr()[user_id].indices]\n",
    "        top_items = [data['item_labels'][i] for i in annoy_member_idx.get_nns_by_vector(np.append(user_embeddings[user_id], 0), 50)]\n",
    "        if print_output == True:\n",
    "            print(\"User %s\" % user_id)\n",
    "            print(\"     Known positives:\")\n",
    "\n",
    "            for x in known_positives[:3]:\n",
    "                print(\"        %s\" % x)\n",
    "\n",
    "            print(\"     Recommended:\")\n",
    "\n",
    "            for x in top_items[:3]:\n",
    "                print(\"        %s\" % x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User 3\n",
      "     Known positives:\n",
      "        Seven (Se7en) (1995)\n",
      "        Indiana Jones and the Last Crusade (1989)\n",
      "        Contact (1997)\n",
      "     Recommended:\n",
      "        Cop Land (1997)\n",
      "        Air Force One (1997)\n",
      "        Contact (1997)\n",
      "User 25\n",
      "     Known positives:\n",
      "        Toy Story (1995)\n",
      "        Twelve Monkeys (1995)\n",
      "        Dead Man Walking (1995)\n",
      "     Recommended:\n",
      "        Men in Black (1997)\n",
      "        Toy Story (1995)\n",
      "        Rock, The (1996)\n",
      "User 450\n",
      "     Known positives:\n",
      "        Kolya (1996)\n",
      "        Devil's Own, The (1997)\n",
      "        Contact (1997)\n",
      "     Recommended:\n",
      "        Hoodlum (1997)\n",
      "        Excess Baggage (1997)\n",
      "        G.I. Jane (1997)\n"
     ]
    }
   ],
   "source": [
    "sample_recommendation([3,25,450], model, movielens, print_output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compare this to the original, non-ANN version here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample_recommendation_original(model, data, user_ids, print_output=True):\n",
    "\n",
    "    n_users, n_items = data['train'].shape\n",
    "\n",
    "    for user_id in user_ids:\n",
    "        known_positives = data['item_labels'][data['train'].tocsr()[user_id].indices]\n",
    "        scores = model.predict(user_id, np.arange(n_items))\n",
    "        top_items = data['item_labels'][np.argsort(-scores)]\n",
    "        if print_output == True:\n",
    "            print(\"User %s\" % user_id)\n",
    "            print(\"     Known positives:\")\n",
    "\n",
    "            for x in known_positives[:3]:\n",
    "                print(\"        %s\" % x)\n",
    "\n",
    "            print(\"     Recommended:\")\n",
    "\n",
    "            for x in top_items[:3]:\n",
    "                print(\"        %s\" % x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "User 3\n",
      "     Known positives:\n",
      "        Seven (Se7en) (1995)\n",
      "        Indiana Jones and the Last Crusade (1989)\n",
      "        Contact (1997)\n",
      "     Recommended:\n",
      "        Contact (1997)\n",
      "        Air Force One (1997)\n",
      "        Cop Land (1997)\n",
      "User 25\n",
      "     Known positives:\n",
      "        Toy Story (1995)\n",
      "        Twelve Monkeys (1995)\n",
      "        Dead Man Walking (1995)\n",
      "     Recommended:\n",
      "        Men in Black (1997)\n",
      "        Toy Story (1995)\n",
      "        Rock, The (1996)\n",
      "User 450\n",
      "     Known positives:\n",
      "        Kolya (1996)\n",
      "        Devil's Own, The (1997)\n",
      "        Contact (1997)\n",
      "     Recommended:\n",
      "        Hoodlum (1997)\n",
      "        G.I. Jane (1997)\n",
      "        Cop Land (1997)\n"
     ]
    }
   ],
   "source": [
    "sample_recommendation_original(model, movielens, [3, 25, 450])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So pretty similar!\n",
    "\n",
    "## But how fast are they, and do they scale?\n",
    "\n",
    "Here are the two functions compared on a single prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 4.56 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "sample_recommendation_original(model, movielens, [3, 25, 450], print_output=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 2.88 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "sample_recommendation([3,25,450], model, movielens, print_output=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this is a bit faster, but at these volumes it probably doesn't justify the extra effort. Where these libraries provide value is against very large numbers of vectors. So let's see how the ANN libraries stack-up versus the Scikit-Learn pairwise distance function, which can also be used for (exact) nearest neighbour searches:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,u'Time (ms)'), Text(0.5,0,u'Numer of vectors')]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4RD7/8zCuTg589FTNXB8OPq/K0QcEa61/x+juYD3tv1avY4HuaSwbmEa2DdJI\nn2Ze+dnrr7/Ot99+m+q8nj3vrTvGx8fzxhtvEBkZiYuLC8WLF2fy5Mk5HaYQIhdZtIUvQr9g9oHZ\ndArqxNhmY3G0d7R1WHlZpntQKKVWAPOUUuMBP6ASsB2jZeqePM1l1pp5LDDzTBpL/DTQBpiplKoG\nuAAXc2ibc42UU0KkzWLRzN5ykk/+OISLoz3f9qrHY7X9bB1Wlg17uCI3bicwad0x3J3seffRagW3\ncnU7JsNJc7RiJTInJubOASxZsiQ3b95Mfp9WV4l169Ylvw4JCcmp0IQQNhZviWfM32NYcWwFvar2\n4q1Gb2GncvRZ7/leVnpQmOkWYQx0kQAM01onAqSWp7nKt4AFSqkPgd1m3gCvAz8opV7F6B74XJa7\nrNuIlFNCpC/y6i1GLdnD5qNRPFylOJ92rU0JTxdbh5VtRnWows24RKZuOoG7swOvtquc/kL50c4Z\nGU4qFSshhMgnbiXcYtT6UayPWM+wusN4ofYLBfcKYTbLYg+KscDYjORpTj/OnYGVrKcfAJo9aOxC\niPxFa81Pu84wZsV+LFrz8dO16NkwoMB9Xyul+O9j1blxO4EJa47g4ezA8y0L2OBJWsPOmRlOLhUr\nIYTIB6JvRzMiZAS7L+xmdJPR9KjSw9YhCSGESCEq5jb/+fkf/tx/nkaBxRjXvQ5lfQru/a92dopP\nutbmZnwiY38/iKuTPX2aFKB7Jk9ugqijGU4uFSshhMjjLty8wNDVQzkRfYLPW31Oh8AOtg5J2JjW\nusBd/c6MfNqTUhRQqw+c5+2f9nLtVgL/6VyVQc3LY18IRsyzt1N82aMut+ISGb18H+7O9jxVz9/W\nYWWPnTPAxQu4lqHk0jFfCCHysNPXTtNvZT8irkcwqc0kqVQJXFxciIqKKvSVCq01UVFRuLgUnHtW\nRP4Ul2Dhf78eYPDsUEoUceGX4c0Z0rJCoahUJXFysGNS7/o0CfLhjcV7+WPfOVuHlHU3LsGBFVAn\n5VhHaZMWKyGEyKMORh1k6OqhxtDqHaZT07emrUMSeYC/vz8RERFcvJjvBxTMMhcXF/z9C8iVcZEv\nnbl6i2FzdxEWfpXnHgrknc5VcXawt3VYNuHiaM/U/sH0nbaN4fN3MbV/Q1pVLm7rsDIvbB5Y4qHB\nc8CnGVpEKlZCCJEH7Ti3g+Ehw/F08mRKuykEeQXZOiSRRzg6OhIUJJ8HIWwt5NB5Xlu0h8REzaTe\n9elcq7StQ7I5d2cHZgxoxLPfb+WFOaHMGtCIxuV9bB3Wg0satKJsUyhRNcOLSVdAIYTIY9acXsPQ\nVUMp5VaK2Z1mS6VKCCHykPj2k+fUAAAgAElEQVRECx+vPMjAmaH4ebnyy/DmUqmy4uXqyJxBjSjj\n7cqgWaHsCb9q65Ae3IkNcPkYNBjwQItJxSoPsre3p27dutSsWZPu3bvf9XyQ1HTu3JmrVzP3oR08\neDAHDhzI1LLp8fDwACAyMpJu3bqlme7q1atMmjQpR2IQIr/56chPvLbuNar6VGVmx5mUci9l65CE\nEEKYzkbf4tnvtzJl/XF6Ny7LTy89RKCvu63DynN8PJyZO7gJRd0d6Td9O4fOZWzwhzxj50xw8Ybq\nTzzQYlKxyoNcXV0JCwtj3759ODk5pftE+t9//x1vb++7pmmtsVgs6a5r6tSpVK9ePUvxpsfPz48l\nS5akOV8qVkIY5+zUf6by/t/v09SvKT+0+wFvF+/0FxRCCJEr1h2+wKNfb+Lg2WtM6FmXsU/VwsWx\ncN5PlRGlvFyYN7gJro729Jm6neMXY9JfKC+IuQgHf4G6vcDR9YEWlXus7uPT7Z9y6PKhbM2zarGq\nvNXorQynb9GiBXv37gWgS5cuhIeHExsbyyuvvMKQIUMACAwMJDQ0lJiYGDp16sTDDz/Mli1bGDly\nJHv27GH8+PFMmDCBCRMmcPz4cY4dO0b//v3ZtGkTrVu3Zty4cdSrV49BgwYRGhqKUoqBAwfy6quv\ncuzYMYYNG8bFixdxc3Pjhx9+oGrV1Puanjhxgl69epGQkEDHjh2Tp588eZLHHnuMffv2sX//fgYM\nGEBcXBwWi4WlS5cyevRojh07Rt26dWnXrh2ff/55FvawEPmPRVv4IvQLZh+YTaegToxtNhZHe0db\nhyWEEAJISLTw1eojfLv2KFVLFWFi7/pUKO5h67DyhYBibvw4uDHPTNlCn6nbWDS0Kf5F8/hzvcLm\nWg1a8WCkYpWHJSQksHLlyuRKyvTp0ylWrBi3bt2iYcOGdO3aFR+fu28IPHz4MDNmzGDSpEmcO3eO\nb7/9FoCNGzfi4+PDmTNn2LRpEy1atLhrubCwMM6cOcO+ffsAkrsWDhkyhMmTJ1OpUiW2bdvGSy+9\nREhISKrxvvLKK7z44ov069ePiRMnpppm8uTJvPLKK/Tu3Zu4uDgSExP55JNP2LdvH2FhYZnfWULk\nU/GWeMb8PYYVx1bQq2ov3mr0FnZKOhMIIURecOFaLMPn72bbics8ExzAmCdq4OokrVQPomIJD2YP\nMga06D11G4tfaEoJzzz6mASLBXbNgrIPQfEqD7y4VKzu40FalrLTrVu3qFu3LmC0WA0aNAiAr7/+\nmp9//hmA8PBwjhw5ck/Fqly5cjRp0gSAUqVKERMTw/Xr1wkPD6dXr15s2LCBjRs38vTTT9+1XPny\n5Tl+/DjDhw/n0UcfpX379sTExPD333/TvXv35HS3b99OM+7NmzezdOlSAPr27ctbb927/5o2bcrY\nsWOJiIjg6aefplKlSg+6e4QoMG4l3OKN9W+wIWIDL9d9mSG1h8hDX4UQIo/YfPQSryzYzY3biXzR\nvQ5dG8jQ/plVw8+LmQMb0WfqNvpM28aCIU0p5u5k67DudXIDXD4Ord/J1OJyWTQPSrrHKiwsjG++\n+QYnJyfWrVvH6tWr2bJlC3v27KFevXrExsbes6y7+903UDZt2pQZM2ZQpUoVWrRowcaNG9myZQvN\nmjW7K13RokXZs2cPrVu3ZuLEiQwePBiLxYK3t3dyLGFhYRw8ePC+saf3o7BXr16sWLECV1dXOnTo\nkGbrlxAFXfTtaF5Y9QIbIzYyusloXqjzglSqhBAiD0i0aL5a/S99pm3D282JFS83k0pVNqhftihT\n+wdzKuom/adv51psvK1DulfoDHAtCtUebNCKJFKxyieio6MpWrQobm5uHDp0iK1bt2ZouZYtWzJu\n3DhatmxJvXr1WLt2Lc7Oznh5ed2V7tKlS1gsFrp27cr//vc/du3ahaenJ0FBQSxevBgwbq7fs2dP\nmutq1qwZCxYsAGDu3Lmppjl+/Djly5dnxIgRPPHEE+zdu5ciRYpw/fr1DG2PEAXBhZsXGPDnAPZd\n2se4VuPoUaWHrUMSQggBXLx+m/7Tt/PV6iM8VbcMK15uRqWSRWwdVoHxUAVfvutTn4NnrzFo5g5u\nxiXYOqQ7Yi7AoV+hTi9wzFxXRalY5RMdO3YkISGB2rVrM3r06OTufulp0aIF4eHhtGzZEnt7ewIC\nAmjevPk96c6cOUPr1q2pW7cuzz33HB9//DFgVJCmTZtGnTp1qFGjBsuXL09zXRMmTGDixIk0bNiQ\n6OjoVNMsXLiQmjVrUrduXQ4dOkS/fv3w8fGhWbNm1KxZk1GjRmVou4TIr05dO0W/lf04c/0Mk9pO\non1ge1uHJIQQAth6PIpHv97IjpOX+bRrLb7oUQc3J7lrJrs9UrUkE3rWY+epK7wwZyex8Ym2DskQ\nNhcsCZkatCKJ0lpnX0D5THBwsA4NDb1r2sGDB6lWrZqNIhKpkWMiCoqDUQcZunooWmu+a/sdNXxr\n2DqkPEEptVNrHWzrOPKi1MopIUT2slg0360/xhd/HSbQx52JvetTrbSnrcMq8BaHhjNqyV7aVS/J\npN71cbS3YXuPxQLf1ANPfxjw2z2zM1pOSYuVEELkgh3ndjDgzwE42zszq9MsqVQJIUQecPlGHANm\n7uDzPw/zaG0/VgxvLpWqXNI9OIAPnqzBqgPneWPxHhItNmzsObEerpzMUmsVyKiAIhPGjh2bfN9V\nku7du/Puu+/aKCIh8rY1p9bw5oY3CSgSwJR2UyjpXtLWIQkhRKEXevIyL8/bzeWbcYx9qia9GpWV\nQYRyWb+mgcTcTuCzPw6z89QV6gZ4U9vfi9r+3tQs44WHcy5VVXbOANdiUD1zg1YkkYpVKrTWcmLd\nx7vvvptrlajC3FW1sNFaExUbRWRMJJExkZyJOcPZG2eN/zFnOXvjLJ7OnlTwqkAF7wpU9K5IBW/j\ntbuje/orsJGl/y7lg60fUNO3JpPaTMLL2Sv9hYQQQuQYi0Xzw8bjfPbnYfyLuvLTiw9Rs4x8N9vK\nS60rUqKIC2sOnmf36av8uvcsAEpBheIe1Pb3oo6/UeGqVtoTF8dsfo7Y9fNw6DdoPBQcnLOUlVSs\nUnBxcSEqKgofHx+pXNmY1pqoqChcXPLoQ+TEA7FoCxdvXiTyRmRy5cn69dkbZ7mdePdz0rycvfBz\n9yPQK5Amfk24evsqx64eY8ehHcRZ4pLTlXYvTXnv8lT0qnhXpcvN0XZPd9daM23fNCbsmkCzMs0Y\n32q8TeMRQggBV2/G8fqiPaw5dIHOtUrxSdfaeLo42jqsQq9bA3+6mUPaX4q5zT8R0eyJuMo/EdFs\n+PcSP+06A4CDnaJKqSLU9k9q2fKicskiWbs/KxsGrUgiFasU/P39iYiI4OLFi7YORWBUdP395dkR\n+UGCJYGLNy/e1dJkXXk6d+Mc8Za7n1lRzKUYfu5+VCpaidYBrSntXpoyHmXw8/DDz8MvzZaoREsi\nETERHL16lONXj3P06lGjwnX23grXXa1bZmtXTldwLNrCF6FfMPvAbDoHdebD5h/iaCcFtxBC2NLu\n01d4ed5uLlyPZczj1en/UKBcRM+DfD2cebhqCR6uWgIwLlSejY5lb0Q0eyOusjcimt/2RjJ/+2kA\nnB3sqOHnaVXZ8qa8rzt2dhk4thYL7JoFgS3At1KWY8/RUQGVUh2BCYA9MFVr/UmK+c7AbKABEAU8\no7U+qZTyAZYADYGZWuuXzfRuwGKgApAI/KK1ftuc9xzwOXDGzP5brfXU+8Unoy0JkXHxlnjO3zh/\nV2UpqRIVGRPJ+RvnSdB3P4/C19UXPw8/yriXobSHUWlKqjyVci+V7RWcBEsCZ2LOJFe0kv6fiD5x\nV6XOz90vucJV3ru88d+rfLbEE2+J5/3N7/PL8V/oXa03bzZ8Ezsl4wTdj4wKmDYpp4TIOq010zef\n5JOVBynp6cLEXvWpE+Bt67BEFmitORV1kz1mReufiGj2RUZzM84Yut3D2YGaZTyp4+9NLbMroX9R\n13sr0kfXwI9PQ9dpUKtbmuvLaDmVYy1WSil7YCLQDogAdiilVmitD1glGwRc0VpXVEr1BD4FngFi\ngdFATfPP2jit9VqllBOwRinVSWu90py3MKkSJoR4cBHXIwi/Hn5PN73IG5FcuHkBi7Ykp1UoSriV\nwM/Dj7ol6uLn7pfc0uTn7kdpj9I422etr/KDcrBzoJxnOcp5lqNN2TbJ0xMsCURcj7hT2Yo+xrGr\nx9h6dutdFa4yHmXuatmq6F2RIK+gDFe4biXc4o31b7AhYgPD6w3n+VrPy9VQIYSwoehb8by5ZA9/\n7j9Pu+olGdetDl5u0oMgv1NKEejrTqCvO0/WLQNAokVz9EJMcqvW3oirzNh8krhE47dLMXcnapXx\nSm7VquPvRYmdM8HNB6o9ni1x5WRXwEbAUa31cQCl1ALgScC6YvUkMMZ8vQT4VimltNY3gE1KqYrW\nGWqtbwJrzddxSqldgPQTEyIbTAybyOQ9k5Pf2yt7SrqVxM/Dj0alGiVXmJIqT6XcSuFonz8KJwc7\nBwK9Agn0CqRNubsrXOHXwzl29Vjy39Hoo2yJ3JJ6hcuqW2F5r/K4Orgmp4m+Hc3wkOGEXQhjdJPR\n9KjSI1e3UQghxN3+iYjmpXk7OXs1lvcercag5kFysasAszfvv6pSqgjdgwMAiEuwcPjcdbNly6hw\nTVx7EYuG4lxli8tvrPHqypENp6nt702tMl4UdXfKdAw5WbEqA4RbvY8AGqeVRmudoJSKBnyAS+ll\nrpTyBh7H6GqYpKtSqiXwL/Cq1jo8leWGAEMAypYtm+GNEaIg++PEH0zeM5nOQZ3pVrkbZTzKUMKt\nBA52Bfs2TAc7B4K8ggjyCqJtubbJ060rXEndCY9FH7urwqVQ+Hn4JVe0Np7ZyMnok4xrNY72ge1t\ntUlCCFHoaa2Zs/UUH/56EF8PJxa+0JQG5YraOixhA04OdtTy96KWvxdQDoBbcYnsj4yGjV/gcCyR\nufGt2fDXv8nLlC3mljwwRtKw7xmVk7+aUrskkPKGroykuTdjpRyA+cDXSS1iwC/AfK31baXUUGAW\n8Mg9mWv9PfA9GH3X01uXEAXd/qj9jN48mvol6vNhsw/zTStUTrpfhev09dPJFa6kgTM2R27Gxd6F\nSW0n0aR0ExtGLoQQhdv12Hje/ukfftt7loerFGd8j7pZaoEQBY+rkz3BZb0hagUEtmD2c72JvhXP\n/jPR7DG7EKYc9j2jcrJiFQEEWL33ByLTSBNhVpa8gMsZyPt74IjW+qukCVrrKKv5P2DcryWEuI9L\nty7xSsgrFHUpyvjW46VSlQ4HOwfKe5WnvFd52pVrlzw93hKP1honeym8hRDCVg5EXmPYvF2cvnyT\ntzpW5YWW5TM2MpwofI6HwNXT0HYMAF6ujjxU0ZeHKvomJ7Ee9v3VT1LPJqWcrFjtACoppYIwRurr\nCfRKkWYF0B/YAnQDQnQ6wxQqpT7EqIANTjG9tNb6rPn2CeBglrdAiAIsLjGOV9a+wrW4a8zuNBsf\nVx9bh5RvyVDqQghhO1pr5m8PZ8wv+ynq5sj855vQKKiYrcMSeVnoDHDzhappD1phPez7qxnMNscq\nVuY9Uy8Df2IMtz5da71fKfUBEKq1XgFMA+YopY5itFT1TFpeKXUS8ASclFJdgPbANeBd4BCwy7wB\nMWlY9RFKqSeABDOv53Jq24TI77TWfLDlA/Ze3Mv41uOpWqyqrUMSQgghHtiN2wn85+d/WB4WSYtK\nvnz1TF18PHJ3RFqRz1w/B4dXQtNh4JC9PU1y9M50rfXvwO8ppv3X6nUs0D2NZQPTyDbVNl2t9TvA\nO5kKVIhCZs6BOSw/tpwX67x4V5c2IYQQIr84fO46L83dyYlLN3i9XWWGPVxRuv6J9O2eAzoRGjyX\n7VnLUyuFKGQ2n9nMFzu/oF25dgytM9TW4QiRK5RSHZVSh5VSR5VSb6cy31kptdCcv00pFWg17x1z\n+mGlVIf08lRKBZl5HDHzdDKnf6mUCjP//lVKXc3ZrRai4FoUGs6TEzdxLTaBHwc3ZnibSlKpEumz\nJMLO2RDUCnwqZHv2UrESohA5EX2CUetHUcm7Eh82+xA7JV8BouCzemB9J6A68KxSqnqKZMkPrAe+\nxBwAyUzXE6gBdAQmKaXs08nzU+BLrXUl4IqZN1rrV7XWdbXWdYFvgJ9yapuFKKhuxSXyxuI9vLlk\nL/UCivLbiOY8VME3/QWFADi2FqJP50hrFUjFSohC41rcNUaEjMDR3pGvH/kaN0c3W4ckRG5JfmC9\n1joOSHpgvbUnMR7TAcYD69so40beJ4EFWuvbWusTwFEzv1TzNJd5xMwDM88uqcT0LMZjQ4QQGRR+\n+SZPTtzE0l0RjGhTiR8HN6ZEERdbhyXyk50zwL04VH0sR7Iv2E//FEIAkGhJ5M31bxJxPYKpHabi\n5+Fn65CEyE1ZeWB9GWBrimXLmK9Ty9MHuKq1TkglPQBKqXJAEBCSWrDyIHsh7nX8Ygy9ftjGrfhE\nZg9sRItKxW0dkshvrp01Bq14aHi2D1qRRFqshCgExu8cz+bIzbzb5F0alGxg63CEyG1ZeWB9dk23\n1hNYorVOTCUtWuvvtdbBWuvg4sXlx6MQh89dp8eUrcQnWlgwpIlUqkTm7P7RGLSifr8cW4VUrIQo\n4JYdXcbsA7PpVbUX3Sp3s3U4QtjCgzywnhQPrE9r2bSmXwK8zTzSWldPpBugEBmy70w0z3y/BXs7\nWPhCU6qV9rR1SCI/siTCrllQvnWODFqRRCpWQhRgYRfC+GDLBzQu3ZhRDUfZOhwhbCX5gfXmCH09\nMR5Qby3pgfVw9wPrVwA9zVEDg4BKwPa08jSXWWvmgZnn8qSVKKWqAEWBLTmwnQLAYoEblyDhtq0j\nEVm089QVnv1hK+5ODix6oSkVS3jYOiSRXx1dA9Hh0GBAjq5G7rESooA6d+McI9eOpJR7Kca1HIeD\nnZzuonDKygPrzXSLgAMYD6AfltSFL7U8zVW+BSxQSn0I7DbzTvIsxmAYKbsHivvRGm5dgZgLEHMe\nblw0/sdcuPt10nudCB6loNcC8Ktn6+hFJmw5FsWgWTsoUcSZuc83oYy3q61DEvnZzpnGoBVVOufo\nalRh/m4PDg7WoaGhtg5DiGx3K+EW/Vf25/T108ztPJcK3jnX7C1EVimldmqtg20dR15UoMsprSH2\n6p0KUXKFKamCZE6LuWi8tiTcm4edI3iUMH4weZQED/O/mw9snQw3L0G3GVClY+5vn8i09f9eZMjs\nUMoWc2Pu4MaU8JSR/0QWXIuEL2tCsxHQdkymsshoOSWXsIUoYLTW/Hfzfzl0+RDfPPKNVKqEELlH\na4iNTqdFyaplKTHu3jzsHMyKUglwLwElaxkVJvcSxjSPEkblyb04uBYFlcZDYWt2g3k9YMGz0Okz\naPR8zm67yBZ/7T/Hy/N2U7GEB3MGNcLHw9nWIYn8btccc9CK/umnzSKpWAlRwEz9Zyp/nPyDkfVH\n0iqgla3DEUIUQDoxgZ1LPqds/AmK20WjrFuaElO5t0nZm5Uls0WpeLU7r1NWmFy8wS4bbgEvUhKe\n+w2WDoLf34Crp6DtB9mTt8gRv+yJZOTCMGqV8WLWgEZ4uTnaOiSR31kSYddsKP8wFAvK8dVJxUqI\nAiTkdAhf7/6azkGdGVhzoK3DEUIUUKdXTyL44Cdc1J4cty+Go1cpipdpgqt36btblJJeuxazTYXG\n2QN6zoOVb8Hf38DV0/DUFHCU+3XymsWh4by1dC/BgcWY/lxDPJzlJ6rIBkdXw7UI6PhRrqxOPrVC\nFBBHrhzhnY3vUNOnJv/30P+h0uoeI4QQWRFzgZLbP+VvSw1OdJ7HsrBIdpy8gv15RZuqJXimYQCt\nKhfHwT6PtAzZ2UPnz6FoOfjrPeMhoc/OB3dfW0cmTHO2nGT08v20qOTL932DcXWyt3VIoqAInWG0\niufwoBVJpGIlRAFwJfYKw0OG4+7ozlcPf4WLg9zoK4TIIX++i11iLItLjeTLJoH0bhLI0QsxLA4N\nZ+muCP46cJ6Sns50a+BPj+AAyvm42zpi4z6sh4aDVwD8/AJMawe9l+To82xExkzdeJwPfztI22ol\n+LZXfVwcpVIlskl0BBz5E5qNBPvc6VaaRy4nCSEyK94Sz+vrX+fizYt89fBXlHQvaeuQhBAF1fF1\n8M8ivkt4nBq17gyQVbGEB+90rsaWd9owuU8Dqpf25Lt1x2j1+Tp6/bCV5WFniI1PtF3cSWp0gf6/\nGANsTG0Lp7faOqK8JfoMzO8Fy4YZzwPLQVprvllzhA9/O8ijtUrzXZ8GUqkS2Wv3j8aAOg1yftCK\nJNJiJUQ+9+n2T9lxbgcfNf+I2sVr2zocIURBlXAbfnuda64BTLryJCurlrgniaO9HR1rlqJjzVKc\njb7FktAIFu0M55UFYXi5OtKlrh/PNCxLdT9PG2yAKaARDFoFc7vDrCfgqclQ82nbxZMXaA3/LDYG\n+Yi7CZZ48PKHh9/JodVpPv/zMJPWHePp+mX4rGvtvNN1VBQMiQnGoBUVHoGigbm2WvkUC5GPLTq8\niIWHFzKgxgAer/C4rcMRQhRkmydA1FGmeLyIn29Ryhf3uG/y0l6uDG9TifVvPMzcwY1pVbk487eH\n0/nrjTzx7SZ+3HqKa7HxuRR8Cj4VjMqVXz1YMgA2fWVULgqjG1GwuD/89DwUrwrDtkGdXrD+Ezj4\nS7avTmvN//1ygEnrjtGrcVnGdasjlSqR/Y6ugmtnoMFzubpaabESIp/acW4HH2/7mBZlWvBK/Vds\nHY4QoiCLOgYbxpFQrQs/7C1P36b3tlalxc5O0ayiL80q+nL1ZhzLdp9hwY5w3lu2jw9/O0DnWqXp\n2bAsDQOL5u6gO+4+0G85LBsKq983hmPv9DnYF6KfRof/gBXD4dYV48GpD40wBvt47Eu4dBh+Hgo+\nFaFEtWxZncWieXfZP8zfHs7AZkGMfqyaDLQkcsbOmcaIpFU65epqC9G3hxAFR8T1CF5b9xoBngF8\n2vJT7O2kX7oQIodobXQRs3dic4XXiNsdQZtUugFmhLebE881C6L/Q4HsjYhmYWg4K8Ii+WnXGcr7\nutOjYQBP1y9DiSK5NACPowt0nQ7eZY0WuegI6DbDGKa9IIu9Bn/+B3bPgZI1oe/PUKrmnfmOLvDM\nXPi+Fcx/Fp4PAbdiWVplQqKFUUv28vPuMwx7uAJvtK8ilSqRM6Ij4Mhf0Py1XBu0Iom0vQqRz9yI\nv8HwkOEk6kS+eeQbijgVsXVIQoiCbP/PcCwEHnmPlacURZwdCA7M2o9spRR1Arz56KlabH+3DeO6\n18HHw4lPVh6i6cchDJkdSsih8yQk5uwACoDxfK12H8Cj441n3szoZAzJXlCd3ASTm0HYXOOH5/Mh\nd1eqkniWhmd+NLpTLRlo3LOSSXEJFobP383Pu8/wRvvKjOpQVSpVIufsmm1cEKrfL9dXLS1WQuQj\nFm3hPxv/w/Ho43zX9jvKeZazdUhCiIIs9hr88Q6UroMleBAha9bTsnJxnByy77qsm5MD3Rr4062B\nf6rDtndvEECP4ADK+rhl2zpT1XCQMRz74ueMEQN7L4aS1XN2nbkpPhZC/gdbJho38w/4A8o2vv8y\nAY3g0S+M7oKr34cOYx94tbHxiQybu4s1hy7w3qPVGNyifObiFyIjEhNg1xyo2MZ4dl0uy9EWK6VU\nR6XUYaXUUaXU26nMd1ZKLTTnb1NKBZrTfZRSa5VSMUqpb1Ms00Ap9Y+5zNfKvOShlCqmlFqllDpi\n/i+ak9smhC1MDJtISHgIo4JH8ZDfQ7YORwhR0K0dCzHn4bEv2X/uJheu3+aRTHYDzIiUw7bX8PNi\n0rqjtPx8be4M2165PQxcCZYEmN4Bjq3NuXXlpsjdMKUlbPnWqEC+uDn9SlWS+v2g0RBj2b2LHmi1\nN+MSGDwrlDWHLvBhl5pSqRI578hfcD0SGgywyeoz1GKllAoGWgB+wC1gH7Baa335PsvYAxOBdkAE\nsEMptUJrfcAq2SDgita6olKqJ/Ap8AwQC4wGapp/1r4DhgBbgd+BjsBK4G1gjdb6E7MS9zbwVka2\nT4j84I8Tf/D93u95utLT9K7W29bhCGETmSmPRCZFhsH2740f4mUasGb1vygFD+dgxSpJymHbl+6M\nYGHonWHbn6pXhh7BATkzbHvpOjB4NczrAXO7weNfQ718+p2bGA8bx8OGz8C9OPRZChXbPng+HT6C\nCweNlivfSsZoium4HhvPoJmhhJ66zLjudejWwD8TGyDEA9o5AzxKQeUONln9fVuslFLPKaV2Ae8A\nrsBh4ALQHFillJqllCqbxuKNgKNa6+Na6zhgAfBkijRPArPM10uANkoppbW+obXehFHBso6nNOCp\ntd6itdbAbKBLKnnNspouRL53IOoAozePpl6Jerzb+F3pmy4KnSyWR+JBWRLh11fBzRceGQ3AmoMX\nqF+2KMXcnXI1lNJerrz8yN3Dts/bdjp52Pa523Jg2HbvABj4BwQ2h+UvwdqP8t9w7Bf/hWntYN1H\nUONpeGlL5ipVYAwA0H0muJeABb0h5sJ9k1+9GUefadvZdfoKXz9bTypVIndcDYcjq6B+31wftCJJ\nei1W7kAzrfWt1GYqpeoClYDTqcwuA4RbvY8AUrY7J6fRWicopaIBH+BSGvGUMfOxzrOM+bqk1vqs\nmddZpVSql9SUUkMwWrwoW1bKYJH3Xbp1iREhI/B28WZ86/E42efujxoh8oislEfiQYVOh8hd8PRU\ncPXm/LVY/jkTzagOVWwWUlrDtr/78z7+9+sBHq3lxzMNA7Jv2HYXL+i1GH4dCes/hSun4IlvwCGP\nfwdbLLB9CqweA45uRoWoxlNZz9fdF3rOhWntYWFf6P9LqvsiKuY2faZt59iFGL7r04B21Utmfd1C\nZMSu2cZ/GwxakeS+FeqSJ2gAACAASURBVCut9cR05ofdZ3Zq32opL/dkJE1W0t+bWOvvge8BgoOD\n89nlJ1HYxCXGMXLtSK7FXWNWx1n4uvraOiQhbCKL5ZF4ENfPw5r/QVArqNUNgLWHjBaKNtVyvhtg\nRlgP2/7PmWgW7DCGbV+6KyJ52PZuDfzx9XDO2oocnOBJc7CHtWONEfKe+RFcvbNlO7Ld1dOw7CU4\nuREqdzS6MRbJxopN6drQZaIxSuDKN+Hxr+6afeFaLL2mbiPiyk2m9g+mZeXi2bduIe4nMcF4fEDF\ntsbjE2wkQ4NXKKU+U0p5KqUclVJrlFKXlFJ90lksAgiweu8PRKaVRinlAHgB9+snH2Hmk1qe582u\ngkldBu/fTi1EHqe15oMtH7Dn4h7+1+x/VPPJngc0CpGfZbI8Eg/ir3ch4ZYx/LjZ8rPm0AXKeLtS\npWTeeryDUora/qkP297i07V8s+ZI1ge7UApavQlPTYHTW41BLa6cyp4NyC5aw+65MOkhY6CKJ76B\nZxdkb6UqSc2u0PxV416W0OnJk89cvUWPKVs4e/UWMwc0kkqVyF1H/oTrZyHYNoNWJMnoqIDttdbX\ngMcwKjeVgVHpLLMDqKSUClJKOQE9gRUp0qwA+puvuwEh5r1TqTK7+l1XSjUxRwPsByxPJa/+VtOF\nyJd+PPgjy48tZ2idoXQItM1NmELkQZkpj0RGHV8H/yw2fjj7VgSM4bL/n737jo+iWh8//nlSIBAg\n9BoQkI4UIYBIBxEEL/zsqF8Lotx7FTsq6LXhtaBYr1iw61VQUa8IKCqhCCJFQIpJMASUhBJC6CUk\n2fP7YybJJmySTdnMbvZ5v155ZfbMmbPPTpI9OTvnPLPijzSGdmjo1+s7c9K2f/6P8/nxnoEMbt+A\n53/YxrDnl/HNb7sp4t8L73QbB9d9ad3j6u0LIGV9+QReVsf2W+uevr7VuqL0z5XWVChf/qyGPgxt\nhsPC++DPn/nzwHGufGMVB46f5qOb+3Be63q+e26lPFn3HtRsAm2d/X/J24FVzgqwUcBsb7IvGWOy\ngEnAIiAO+MwYs1VEponIGLvaO0A9EUkE7sHK5AeAiOwEXgBuFJFkEcm5mcQ/gbeBRGA7VkZAgGeA\n4SLyB1Ymwme8fG1K+Z2fU35mxroZDGsxjH92+6fT4SjlT0rcHykvZZ6C+fdAnVbWjWNtvyQd4GRm\nNkP9ZBqgN9o0rMnr/9eT2becR1S1cG6fvYEr3ljFpuRDZWu41UCY8D2ERcD7oyHh2+KP8aW4b+C1\nPtaNjS98Em6Yb01b9LWQULjsbajTkqw513Hb699w4nQWs285jx4t9G43qoId/NP6Gzj3Ogh19ha9\n3j77NyISj5Xa9lYRaUCBjH2eGGMWYqVEdy97xG37FHBFIce2LKR8HWemYMcYcwAYVlxMSvm7nYd3\nMnn5ZNrUbsNT/Z8iRHx6uzmlAk2p+iPlhZUvQ/p2+L8vITwitzg2PpVq4aH0DcCrEH3Prsc3t/dn\n7q+7eG5RAmNeXcllPaK5f2R7GtWKKL4BTxp2yEvHPucauOhZ6H1L+QZenJOH4Lsp8NtsKz38JW9C\nwwqeLl6tNolDZ9H489E8x3TCbllE22ZRFRuDUmCtrRJxNGlFDq/+YzPGTAH6AjHGmEzgOGemTldK\nldGR00e4PfZ2wiSMV4a+QvXw6k6HpJRf0f7IRw5sh5+et9Jyt8n7jNIYw+K4VPq3rU9EeKiDAZZe\naIhwVa8WLJk8mH8MOptvftvNkBlLeTW2DOuvajaC8QutaUcLJ8Oih6xsfBVh+xJ4/XzrZr2DHoCb\nF1f8oAr4bdchLpt7gMfD7qIDO2j7y0OBl5JeBb7sTFj/kTU1tXbz4uv7mLc3CA7FuiFjSzvJRI4X\nfBKVUkEo25XN/cvvJ/loMm9d+BbNajQr/iClgoz2Rz5gjDU4CK1i3QjWTcK+o6QcOsntQ9s4FFz5\nqRkRzpSLOnB17+Y8vTCeGd9vY/aaXUwd1YHRXZqUfP1YlUgr/fh3U2DVq1ZGvktnQXg137yA0yes\nFOpr3oR6bWHCDxDd0zfPVYy1O9MZ/95a6kSGc8fNdyBbQiH239Yar/NvdyQmFaS2fQfH9kLPF52O\nBPB+jdU3wI1Y95iq6fallConL61/iZUpK3nwvAeJaRzjdDhK+Svtj8rb1q9geywMexhqNcm3a3Gc\nlWB3SIfAWV9VnLPqRfLGddb6q1rVwpn0yQaufHMVm5MPl7yxkFBrKuCIp6z1Th/8DY4XdivOMkhe\nB28OsAZVff4Jf1/u2KBqZWIa17+zhoa1qvL538+ned3qMGAydBoLPzwCiYsdiUsFqV/fh5pNoe2F\nTkcCeL/GKtoY09WnkSgVxL5O/Jr3t77PuPbjuKKdx2WHSimL9kfl6dRh+G4qNOkOvW4+Y3dsfCpd\nmkWVfj2SH+t7dj3m396fz9ftYsb3CYyZuYLLekRz34gSrr8Sgb63QVQ0fDnRyhh47dzcrIplknUa\nlj9rTdOs2RSunwetB5W93VKKjd/HP/67ntb1I/loQh8a1LTvEyYCY1+DtESYOx5uWQL1znYsThUk\nDv5pDeQHPeB40ooc3l6x+lZE/GMoqFQl89v+33h81eP0adyH+3vf73Q4Svk77Y/KU+yTcGwfXPyi\ndfXFTfrx06z/6yBDK9HVqoJCQ4Rxva31VxMHtmbeRmv91cwliSVff9VprJWVL+MIvHMB/LmqbMHt\n+x3eHgbLn4Ou4+DWnx0dVH27eQ9//+hX2jeqyexbzssbVOWoWgOu/gQkxErqkXHUmUBV8Fj/gZ20\n4jqnI8nl7cDqF+ArETkpIkdE5KiIHPFlYEoFg73H93LXkrtoVL0RMwbNIDwkvPiDlApu2h+Vl90b\nYO1b1pWqZj3O2L00IRVjYFgApVkvrZoR4Uy9qCM/3DOQAW3r89yiBIY9v4wFm/aU7P5XzXtZGQOr\n1YUPx8KWL0oejCsbVr4CswbBkd1w1cdwyesQ4VzGvf9tSGHS7A10ja7Nx7f0oU5kFc8V67SEKz6A\ntD/gq39UXEIPFXyyM2HDf60pgFHRTkeTy9uB1fNYWZiqG2NqGWNqGmNq+TAupSq9U1mnuHPJnZzI\nPMF/hv6H2hG1nQ5JqUCg/VF5cGXD/LshsoG1tsqDxfGpNKhZlXOaBk8K7bPqRfLmdTF8cksfalUL\n57ZP1nPVm7+wJaUE66/qtrYGV03Phbk3wYoXvc+Wl74D3r8YfnjY+ofx1l+g48WlezHlZM6av7j7\ns430blmXD2/qTa2IYj4AbD0IRjwJ8fOtaYxK+ULCt9bV9p7jnY4kH28HVn8AW0yZb1uulAIrhfEj\nPz9C3IE4pg+cTps6gZ9xS6kKov1ReVj3rnXFasRTHq+EZGa7WJ6wn6HtGxISUsJseZXA+WfXZ/7t\n/Xn60i5s33+Mv726gvs+/43UI17eMq16Xbj+ayt9/Y+PWYPY7KzC6xtjLcJ/vR/s2wL/7w246r9Q\no0F5vJxSe3/lDqZ8uZmBbRvw3vheRFb1ch1Ln39At2tg6dMQN9+3Qarg9Ot7UKsZtLnA6Ujy8XZg\ntQdYKiJTReSenC9fBqZUZfbOlnf4dse33NHjDgY3H+x0OEoFklL1RyIyUkQSRCRRRKZ42F9VRD61\n968WkZZu+6ba5QkiMqK4NkWkld3GH3abVdz2XSkiv4vIVhH5pAznofSO7oPF06D1YDjnMo9V1u5M\n52hGVlBMAyxMaIhwde8WLLlvMBMHtOZ/G1NKtv4qPAIuewf63WX9Ezh7nOd1R0f3Wjcb/uZOK9Pf\nP3+G7ldba0cc9PrS7Tz2ze+M6NyIWdf3LNl9zESsdXvNesJXf4fUON8FqoLPwZ1WJtMe1/tN0ooc\n3g6sdgCLgSpoelulymTJX0t4Zf0rXNTqIiacM8HpcJQKNCXuj+x7X80ELgI6AVeLSKcC1SYAB40x\nbYAXgen2sZ2AcUBnYCTwmoiEFtPmdOBFY0xb4KDdNiLSFpgK9DPGdAbuKu1JKJNFD0LWKRj1fKH/\nvC+OS6VKWAj92tSv4OD8T62IcKaO6sgPdw+iXxtr/dUFLyxj4WYv1l+FhMDwx61BxvZYeO8iOLIn\nb/+WL+G182DHchg5Ha772vGbnBpjeOGHbUz/Lp4x3Zry6jU9qBpWiptDh0dYV92qRMLsq+FEevkH\nq4LTrx9YSVLO9Z+kFTm8GuYZYx73dSBKBYPEg4lM+WkKHet1ZNr500p+Q0qlglwp+6PeQKIxJglA\nROYAY4Hf3eqMBR6zt+cCr4r1BzoWmGOMyQB2iEii3R6e2hSROGAocI1d5wO73deBW4CZxpiD9mtJ\nLcVrKZvtS2DLXBg0pch04LHxqfRtXc/7qV9BoGX9SGZdH8PPiWlMm/87t368nt6t6vLIxZ04p1kx\n69BiboKo5vDZDVamv0vfsqZjbpkLTXvAJW9Cg3YV80I8OHE6i627j/DbrkP8knSAH+NSuTImmqcv\n7UpoWaaC1mpqDa7eHw1fTIBrPve7KwwqwOQmrRgBUc2cjuYMRf52i8gs4D/GmM0e9kUCVwEZxpiP\nfRSfUpXG2r1reWD5A1QPr87LQ14mIqzy3RdGKV8pY3/UDNjl9jgZ6FNYHWNMlogcxroJcTOsTITu\nx+b05p7arAccMsZkeajfzo53JRAKPGaM+c7D65kITARo0aKFh5dTSpmnYMG9VnKF/ncXWi1p/zF2\npB1nfL+W5ffclcj5beqz4I4BfLp2F89/n8DfXl3BFT2jmTyiPQ1rFvG+3nY43PQtfHIVvD8KQsJg\nyEPQ/54KHWxkZGUTv+com1IOs2nXITYlH+aP1KO47ItvTaIiuG3I2dw7vH35rK9r3htGPw/zbofF\nj8GF/y57myp4JSyE46kQ419JK3IU95f8GvCwiHQBtgD7gQigLVALeBfQQZVSRchyZfHGb28wa9Ms\nzqp1Fs8Pfp7GkY2dDkupQFOW/sjTf4cF53AVVqewck9T6YuqD1af2xYYDEQDP4nIOcaYQ/kqGzML\nmAUQExNTfkk6Vr4E6dvhuq+saVqFiI23LqQNaR+866uKExoiXNOnBRd3a8KrsYm8t3IHCzbt4bah\nbbipX6vC1yM16WZlDPzpBeveO03P9WmcWdkuEvcfY9Ouw2xKsQZR8XuOcjrbSoNeN7IKXaOjGHFO\nY7pFR9ElOqrowWFp9bge9myCn/8DjbtC1yvL/zlUcFj3HtSK9rukFTmKHFgZYzYCV4pIDSAGaAKc\nBOKMMQkVEJ9SAW3v8b08sPwB1qeuZ8zZY3ioz0NUD6/udFhKBZwy9kfJgPvClWhgdyF1kkUkDIgC\n0os51lN5GlBbRMLsq1bu9ZOBX4wxmVjTChOwBlpri4m/7A5st/6ZP+cyOHtokVUXx6XSvlFNmtfV\n96ri1IoI58FRHbmmdwueXBjHs98lMHvNXzx4UUdGntPY83TvqGi4+IVyj8XlMvyZfoJNyYf4bddh\nNqccYkvKEU7aiTZqVg2jS3QU4/u3pFt0bbpGR9GsdrWKm5I+8mkricW826F+W58PKlUllJ4ESUtg\n8INn3NDcX3i7xuoYsNS3oShVucT+FcvDKx8my5XFU/2f4m9n/83pkJQKeKXsj9YCbUWkFZCClYzi\nmgJ15gE3AKuAy4FYY4wRkXnAJyLyAtAUayC0BuvK1Blt2scssduYY7f5tf0c/wOuBt4XkfpYUwOT\nSvhaSs4YawpgWFUrvXoRDp/MZO3OdG4Z2NrnYVUmLetH8tb1MaxMTOOJ+b/zz5KsvyoFYwy7D5+y\npvKlHGZTsnU16ugpawZqRHgInZtGMa53c7pF16ZLdBSt6kU6mzo/NByu/ABmDYE518LEpVCjkl0V\nPbbfuhpcVfO7+cT6D0FCrau9fkpXECpVzjKyM3h+3fPMjp9Nx7odeW7Qc5xV6yynw1IqaNlrpiYB\ni7DWNr1rjNkqItOAdcaYecA7wEd2cop0rIESdr3PsBJdZAG3GWOyATy1aT/lA8AcEfk3sMFuG7vu\nhSLyO5AN3GeMOeDr18/WL61PeS96DmoWPQ35pz/2k+UyDOtQyf7hrSD92lj3v/p03S6e/34bf3t1\nBVf2bM69I9qVaYpd2rEMtytR1kAq7dhpAMJDhQ6Na/G3bk3pFh1F1+jatG1Yg7BQbxM/V6DI+jDu\nY3jnQvjserh+HoRVKf44f7d7A6x8BX7/nzWoGjAZek8scsqtKqGs01bSinYjraQofkqC+R6LMTEx\nZt26dU6HoSqRpMNJ3L/sfhIOJnBdp+u4q8ddVAmtBJ2GUj4kIr8aY2KcjsMflbmfOnUYXu0FNZvA\nLbHFTp+559ONLElIZd2/hpctG5zi8MlMXo39g/d/3knVsFBuG9KG8f1aFns/qMMnM9mScpjfkg9Z\na6OSD7H7sHVj4hCBNg1r0DW6tr0mqjYdGtcs2T2m/MGWL2DuTVa2xItfdDqa0jEGEhfDzy9b6fKr\n1ISeN8D+BEj8AaJawLCH4ZzLrbT7qmy2fgWf32hllmx3YYU/vbf9VImuWIlIpDHmeOnDUqpyMsbw\nv8T/8fSap4kIjWDmsJkMjB7odFhKVVraH3kp9t9wLBWunlPsoCrbZViSkMqQ9g11UFUOoqqF89Do\nTlzT5yyeXBDH9O/i+WTNn/nWX+WkOd+UnDedb0da3q91y3rV6dmyLjfZV6I6N61VOVLgn3MZ7N0M\nK16Exl2sAVagyDptDQx//g+kbrU+tBg+DXreCBH2tM+kpfD9w/DlLbDqVRj+BLQe5GTUge/X961b\nFrQZ5nQkRfLqr1NEzgfeBmoALUSkG/B3Y8ytvgxOqUBw7PQxnvjlCRbuWEivxr14uv/TNIps5HRY\nSlVK2h+VQMp6WPs29L4FmvUotvqGvw5y8EQmQzvqNMDy1Kp+JG/fEMOKP/LWX3WLjiIjy8W2ffnT\nnHeNjuLyntF0jY6ia7PaRFUPdzZ4Xxr6MOzdAgvvgwYd4ay+TkdUtFNHYP0HsOo1OLrbinnsa9Dl\nijOnM7YeDBOXwebPIfYJ+HAMtBluDcAaFbw3uSrWge3WYHXIv/w2aUUObz/2eBEYgbW4F2PMbyKi\nH8eroLc1bSv3Lb+PlGMpTOo+iZu73Eyon//RKxXgtD/yhisb5t8NkQ1g6L+8OmRxfCphIcKAtg18\nHFxw6t+2Pgvu6M+ctbv4aNWfNKkdwYWdfZzm3J+FhMJlb1s3TP7sOiuZRVS001Gd6cgeWP26leY7\n4wi0HAB/e9m6L1lRGRVDQqDbVdBpLKx5E5Y/D2/0g+7XwpAH/XqdkN9Z/4GVtOLc/3M6kmJ5fT3Z\nGLOrQErO7PIPR6nA4DIuPvr9I15a/xL1q9XnvRHv0aNR8Z8IK6XKTvsjL6x7F/ZshMveyZueVIzY\nuFR6taxLVLVKfJXEYWGhIfzfeWfxf+dpQiMAqtWGcZ/AW8OsTIE3fQfh1ZyOypIaZ0332/QZmGxr\ngHT+HV5d/c0nPAL63QnnXgfLZ8CaWbB5Lpw/ySrXDIJFyzoNGz6G9hdBrSZOR1Msb1fT7bKnXxgR\nqSIik4G44g4SkZEikiAiiSIyxcP+qiLyqb1/tYi0dNs31S5PEJERdll7Edno9nVERO6y9z0mIilu\n+0Z5+dqUKpH0U+nctvg2ZqybwcBmA5n7t7k6qFKq4pSqPwoqR/fC4mnQeoi1lsULu9JPkLDvKMN0\nGqCqaA3aw2VvwZ7f4Js7raQQTjEGdvwEH18Br50HW7601k7dvh6ueL/kgyp31evCyKdg0lroMAqW\nPwcvd4c1b0F2Znm9gsonfj6cSIOe452OxCveXrH6B/Ay0AzrBoffA7cVdYCIhAIzgeH2MWtFZJ4x\n5ne3ahOAg8aYNiIyDpgOXCUinbBS3XbGum/IjyLSzr4JZHe39lOAr9zae9EYM8PL16RUia3es5qp\nP03lcMZhHuzzIOPaj6u4mysqpaAU/VHQWfQgZGXA6OeLnqrkZklCKgBDNc26ckL7i2DoQ1aylcZd\n4PzbK/b5XdkQN89Kmb57PVSvZ92EttfNEFmvfJ+rbiu4/F047zb44WFYOBlWvwEXPAYdLvb6bzZo\n/PqelWHx7CFOR+IVb28QnAZcW8K2ewOJxpgkABGZA4zFuhdIjrHAY/b2XOBVsf5LHQvMMcZkYN2d\nPtFub5XbscOA7caYP0sYl1IlluXK4rWNr/H25rc5q9ZZvH7B67Sv297psJQKOqXsj4LH9lgrY9ng\nqVDvbK8PWxyXSqv6kbRuUMOHwSlVhAGTrUyBPzwCDTtVTPa30ydg48dW5r6DO6Fuaxj9AnS/xvdT\nEqN7wo0LYNt38MOj8On/QfPz4MInoHlv3z53oDiw3UplP9T/k1bk8DYrYCvgdqCl+zHGmDFFHNYM\n2OX2OBnoU1gd+waOh4F6dvkvBY5tVuDYccDsAmWTROR6YB1wrzHmoIfXMhGYCNCiRYsiwlfKsvvY\nbh5Y/gAb92/kkjaXMKX3FKqHV3c6LKWCUin7o+CQeQoW3At1z4Z+d3l92PGMLFZtP8D1fXXdj3KQ\niJVlLy3RusfVxCXWQMcXjqdZa53WvAUn06FZjJUSvcPoiv0HXsS6WtdmOGz4CJY8Be8Mt9ZzDXu0\nRB+OVEq/vm8nrbjO6Ui85u1UwP9h3Tn+G8Dl5TGermUWnDhbWJ0ijxWRKsAYYKrb/teBJ+x6TwDP\nA2fcGMEYMwuYBdaNFwsPXyn48c8feeTnR3AZF9MHTGdUa126p5TDStMfBYeVL0F6Elz3P2vBvLeH\nJaZxOtuladaV86rWgKs/gVmDYfY1cPMP5Zvc4cB2WDXTukqVdQraXQT97oAWfZ2dghcaBjHjrdTt\nq161piTGL4CYCTDofois71xsTsnKsH5O7S+Cmo2djsZr3g6sThljXilh28lAc7fH0cDuQuoki0gY\nEAWke3HsRcB6Y8y+nAL3bRF5C5hfwniVynUq6xQz1s3g04RP6VyvM88NfI7mtZoXf6BSytdK0x9V\nfge2w0/PwzmXl3gtwuK4VGpWDaNXy7o+Ck6pEqjT0koU8dGl8NU/4MqPrNTlZZG8Dla+DHHfQGg4\ndL3KWsfVwM+m9FetAYOnWAkzlj5j3Yfut9nQ/y4471b/yZhYEeLnw4kD1oAzgHj7m/qyiDwqIn1F\npEfOVzHHrAXaikgr+wrTOOz7jriZB9xgb18OxBpjjF0+zs4a2ApoC6xxO+5qCkwDFBH3HIyXAFu8\nfG1K5ZN0KIlrFl7DpwmfckOnG/jooo90UKWU/yhNf1S5GQML7oGwajDiqRId6nIZYhNSGdi+AeGh\nZfznVany0nowjHjS+ud6+bOla8PlgoTv4N2LrHtl7VgG/e+GuzbD2Ff9b1DlrmZj+NtLcOsqaNnf\nyvL5n55W2nFXkNxdYt17ULsFtB7qdCQl4u0Vqy7AdcBQ8qZeGPuxR/aaqUnAIiAUeNcYs1VEpgHr\njDHzsKZzfGQnp0jHGnxh1/sMK9FFFnCbMSYbQESqY2Ua/HuBp3xWRLrbce30sF+pIhlj+CrxK55e\n/TTVw6vz2rDXGBA9wOmwlFL5lbg/qvS2fAFJS2HUDKjZqGSH7j7M/qMZDNNsgMrf9PkH7NkES5+G\nRudAx4u9Oy4rw7r31M//gbQEqBVtfeDQ4/rAu2dUg/Zw9WzYuQK+fxi+vhV+eQ2GPw5tLnA6Ot9J\nS4SdP8HQh8t+tbKCeTuwugRobYw5XZLGjTELgYUFyh5x2z4FXFHIsU8CT3ooP4GV4KJgeeCsbFN+\n5+jpo0xbNY3vdn5HnyZ9eLr/0zSo3sDpsJRSZypVf1RpnTpspVdvei7EnLGsuFiL41IRgcHtdWCl\n/IwIXPyiNTj66u9Q70do2LHw+icPWTfGXv0mHNsLjbrApW9B50us6X+BrGV/uHkx/P4V/Pg4/Pcy\n6z51w6dBk65OR1f+1r8PIWEBlbQih7cDq9+A2kCqD2NRyhGb92/mvuX3sff4Xu7scSfjO48nNEDS\neioVhLQ/chf7bzi+H675tFTZzGLjU+nRog51I6v4IDilyig8Aq76r5XMYs41cEssVKuTv86hXfDL\n67D+Azh9zBpwXPK69b0y3RMqJMS64XeHi2HtO9YUyTcHQrdxMOQhqF1JlixkZcDGT6D9qBJfgfcH\n3g6sGgHxIrIWyMgp1PS2KpC5jIsPtn7AK+tfoUH1Brw/8n26N+zudFhKqaJpf5QjZb2VLrr3ROuK\nVQntO3KKzSmHuW+EH681UapWU2tw9f5oKw37NZ9bWfT2bram+235wlpneM6lVkKKJt2cjti3wqpC\n31ute22teAF+eQO2fAnn/RMG3AMRUU5HWDZx31hJK3re6HQkpeLtwOpRn0ahVAVLO5nGv1b8i5W7\nVzL8rOE82vdRoqoG+JuRUsFB+yOwFrDPvxtqNIKhD5WqiSXx1kW/CzoG3qfCKsg07w2jn4d5t8PX\nt8HxVOtm2OGR1gcL5/3TSnQQTKrVtqYC9roZYp+0brew/kMrPXvMBAgL0KvQv75vZYZsXbLspv7C\nq4GVMWaZrwNRqqKs2r2KqT9N5ejpozx83sNc0e4KpDJNF1CqEtP+yLb2HdizES5/t9SfUC+OT6VZ\n7Wq0a1SjnINTygd6XG8ls1j7lvWBwrBHrHWFBacGBpvaLeDSN62rWN8/DN9NgdVvWDcY7nxJYE2H\nTPvDSlox7NGAS1qRo8iBlYisMMb0F5Gj5L+5rwDGGFPLp9EpVY4yXZnM3DCTd7e8S6uoVsy6cBbt\n6rRzOiyllBe0P3JzdC/EPgFnD4XOl5aqiVOZ2az4I40rYqL1gyUVOEY+A53GQPM+1pQ4ladJN7j+\na0hcDD88AnPHWzcbvvDfcNb5TkfnnV/ft5JWdL/W6UhKrbgrVpEAxpgAy0+pVH4px1K4f/n9bNq/\nicvaXsYDvR+gWlgQ3WhPqcCn/VGORQ9aC7xHzSj1p9Grkg5wMjOboZpmXQWS0DBoNdDpKPyXCLS9\nwLpJ+G+zreQ20ZzNIgAAIABJREFU710E7UfDBY9BAz/+MDnzlJW0osPogExakaO4gZUpZr9Sfm/R\nzkU8/vPjGAzPDXyOka1GOh2SUqrktD8C69PoLV/A4Aeh3tmlbiY2LpVq4aGc1/qMu5copQJdSCic\n+3/WFe1fXoMVL8Fr51lZBWs1hdAq9leY23Z4/u2QcM/lud89lIeEl34KX9w3cDIdeo4v33NRwYob\nWDUUkXsK22mMeaGc41Gq3JzKOsWza5/l822f06V+F6YPnE7zmpUkHalSwUf7o8xTsHAy1GsD/e8q\ndTPGGGLjU+nftj4R4XprCaUqrSrVYeBk6HGDlZ5906fW+0h2RvHHllZImIdBWXjxg7k9m6ykFa0G\n+S62ClDcwCoUqIE1h12pgJF4MJH7lt9H4qFExp8zntvPvZ3wkAC/QaBSwU37oxUvQnqStY6iDOtL\nEvYdJeXQSW4f2qYcg1NK+a0aDWDUc9YXWOnpXdmQfdr+ygRXZt62e3nud0/lp8GV5bk83zEejnVl\nQeZJ6ybn2ZkQXg0G3BuwSStyFDew2mOMmVYhkShVDrJd2Xzxxxc8u/ZZIsMjeeOCN+jXrJ/TYSml\nyi64+6O0ROueNV2ugNaDy9TU4jgrzbqur1IqSInYV47CgOpOR1OpFDewCt5PBlXAOHL6CD+n/Mzy\n5OWsSFnBwYyD9G3Sl6cGPEX9avWdDk8pVT6Ctz8yBhbcA2HV4MIny9xcbHwqXaOjaFgrohyCU0op\nlaO4gdWwColCqRIwxrDj8A6WJS9jefJyNqRuINtkE1U1iv7N+jOk+RCGnzWcEAnsy8lKqXyCtz/a\n8gXsWGZlASxjtqz046dZ/9dB7hzWtpyCU0oplaPIgZUxJr2iAlGqKBnZGazbuy53MJVyLAWAdnXa\nMf6c8QyKHkSX+l0IDdGF2EpVRkHbH7my4bup0LSHdTPUMloSn4oxMKxD4KYzVkopf1XcFSulHLPv\n+D5+SvmJZcnLWL1nNSezThIRGkGfJn246ZybGNBsAE1qNHE6TKWU8p2je+BEBlz7uZVCuYxi41Np\nWLMqnZsGz/2UlVKqoujASvmNbFc2Ww5sYXnycpYnLyc+PR6AppFNGXP2GAZGD6R3495EhOm6AKVU\nkDieBr3vhabdy9zU6SwXy7ftZ3TXJoSEBO+SNaWU8hUdWClHHT19lJW7V/JT8k+sSFlB+ql0QiSE\n7g26c1ePuxgYPZA2tdsgov8EKKWCUGgYDHmoXJpatzOdoxlZmg1QKaV8RAdWqkIZY9hxZAfLdy1n\necpyNuzbQJbJIqpqFP2a9mNQ9CD6NetHVNUop0NVSlUiIjISeBnrflhvG2OeKbC/KvAh0BM4AFxl\njNlp75sKTACygTuMMYuKalNEWgFzgLrAeuA6Y8xpEbkReA5IsZ/2VWPM20UGXq8tRJTPtL3F8alU\nCQuhXxvNlqqUUr6gAyvlc6ezT7Nu7zqWpyxn2a5lJB9LBqBtnbbc0PkGBjW3Ek+Eheivo1Kq/IlI\nKDATGA4kA2tFZJ4x5ne3ahOAg8aYNiIyDpgOXCUinYBxQGegKfCjiLSzjymszenAi8aYOSLyht32\n6/YxnxpjJnkdfBluBFxQbHwqfVvXI7KqvtcqpZQv6Lur8onUE6n8lPwTy5OXs2rPKk5mnaRqaFX6\nNOnDjZ1vZGD0QE08oZSqKL2BRGNMEoCIzAHGAu4Dq7HAY/b2XOBVseYgjwXmGGMygB0ikmi3h6c2\nRSQOGApcY9f5wG43Z2DliKT9x9iRdpyb+rV0MgyllKrUdGClyoXLuNiSlpd4Ii49DoDGkY1zE0/0\natyLamHVHI5UKRWEmgG73B4nA30Kq2OMyRKRw0A9u/yXAsc2s7c9tVkPOGSMyfJQH+AyERkIbAPu\nNsa4twGAiEwEJgK0aNHCy5dYtNj4VACG6PoqpZTyGR1YqVI7evooq3avYlnysnyJJ7o16MadPe5k\nYPRA2tZuq4knlFJO8/QmZLysU1i5pzuQF1Uf4BtgtjEmQ0T+gXU1a+gZlY2ZBcwCiImJKRhnqfwY\nt48OjWsSXad6eTSnlFLKA58OrHy0WHgncNQuzzLGxNjldYFPgZbATuBKY8xBX76+YPXtjm+Zu20u\n6/etJ8tkUatKLfo1sxNPNO1H7YjaToeolFLukoHmbo+jgd2F1EkWkTAgCkgv5lhP5WlAbREJs69a\n5dY3xhxwq/8W1losnzt8MpO1Ow/y94GtK+LplFIqaPlsYOWLxcLGmGz7uCHGmLQCTzkFWGyMeUZE\nptiPH/DV6wtGp7JO8dTqp/gq8StaRbXi+s7XMyh6EF0bdNXEE0opf7YWaGtn60vB6l+uKVBnHnAD\nsAq4HIg1xhgRmQd8IiIvYPVHbYE1WFemzmjTPmaJ3cYcu82vAUSkiTFmj/18Y4A4X71gd8u37Sfb\nZRjWUacBKqWUL/nyv2FfLBZeVcTzjQUG29sfAEvRgVW52XVkF/csu4f49Hhu6XILt3W/jdCQUKfD\nUkqpYtlrpiYBi7BmULxrjNkqItOAdcaYecA7wEd2f5OONVDCrvcZVt+VBdyW8yGfpzbtp3wAmCMi\n/wY22G0D3CEiY+x20oEbffzSAWt9VZ3q4XRvXqcink4ppYKWLwdWvlosbIDvRcQAb9pz0QEa5XwS\naIzZIyIeP5rzxaLgyi72r1j+teJfiAgzh81kYPRAp0NSSqkSMcYsBBYWKHvEbfsUcEUhxz4JPOlN\nm3Z5EnmZA93LpwJTSxp7WWS7DEsSUhnaviGhIbreVSmlfMmXAytfLBYG6GeM2W0PnH4QkXhjzHJv\ng/LFouDKKsuVxX82/Id3t7xLp3qdeGHwCzSr0az4A5VSSvmFDX8d5NCJTIbqNECllPI5T1mNyktJ\nFgvj7WJhY0zO91TgK/I+FdwnIk3stpoAqeX4WoJO2sk0Jv4wkXe3vMsV7a7gw4s+1EGVUkoFmMXx\nqYSFCAPbNXA6FKWUqvR8ObDKXSwsIlWw5qvPK1AnZ7EwuC0WtsvHiUhVe2FwW2CNiESKSE0AEYkE\nLgS2eGgrd7GwKrlf9/3Kld9cyeb9m3my/5M80vcRqoZWdTospZRSJRQbl0rvVnWpFRHudChKKVXp\n+WwqoC8WC4tII+Ar+75IYcAnxpjv7Kd8BvhMRCYAf1HIXHlVOGMMH/7+IS/++iLRNaN5Y/gbtKvT\nzumwlFJKlcKu9BMk7DvKv2I6Oh2KUkoFBZ/myC7vxcL2guBuhdQ/AAwrY8hB6+jpozyy8hF+/OtH\nLmhxAdP6TaNmlZpOh6WUUqqUYuOtGfHDOjZyOBKllAoOevMhxbaD27hn6T0kH01mcsxkru90PfZV\nQaWUUgFqcXwqretH0qp+pNOhKKVUUPDlGisVAOZtn8e1C67lROYJ3hnxDjd0vkEHVUopFeCOZ2Tx\ny/YDDO2g2QCVUqqi6BWrIJWRncEza55h7ra59Grci2cHPkv9avWdDksppVQ5WJGYxulsl6ZZV0qp\nCqQDqyCUfDSZe5fdy+8HfmfCOROYdO4kwkL0V0EppSqL2LhUakaE0atlXadDUUqpoKH/TQeZ5cnL\nmfrTVIwxvDLkFYa0GOJ0SEoppcqRy2WITUhlULsGhIfqjH+llKooOrAKEtmubGZunMlbm9+iQ90O\nvDDoBZrXal78gUoppQLKlt2H2X80g2E6DVAppSqUDqyCwIGTB3jgpwdYvWc1l7a9lKm9pxIRFuF0\nWEoppXxgcVwqIQKD2unASimlKpIOrCq5jakbuXfZvRzOOMy086dxSdtLnA5JKaWUDy2O30ePFnWo\nG1nF6VCUUiqo6OTrSsoYw39//y/jvxtPlZAq/HfUf3VQpZRSldzew6fYknJEswEqpZQD9IpVJXQ8\n8ziP/vwoi3YuYnDzwTzZ/0lqVanldFhKKaV8bElCKgDDOjRyOBKllAo+OrCqZBIPJnL30rv56+hf\n3N3zbsZ3Hq83/FVKqSCxOC6VZrWr0a5RDadDUUqpoKMDq0pkftJ8pq2aRvWw6rx94dv0atzL6ZCU\nUkpVkFOZ2axMTOPKmGj9QE0ppRygA6tK4HT2aZ5d+yyfJnxKj4Y9mDFoBg2qN3A6LKWUUhVoVdIB\nTmZmM7SjTgNUSikn6MAqwO0+tpt7l97LlgNbuLHzjdzR4w7CQ8KdDksppVQFi41LpXqVUPq0qut0\nKEopFZR0YBXAVqSsYMpPU8h2ZfPS4JcYdtYwp0NSSinlAGMMsfGp9G9Tn4jwUKfDUUqpoKTp1gNQ\ntiubmRtncuuPt9KwekPmXDxHB1VKKRXE4vceJeXQSYZpmnWllHKMXrEKMAdPHWTKT1P4effPjDl7\nDP86719UC6vmdFhKKaUcFBtvpVkf0l4HVkop5RQdWAWQTfs3ce+ye0k/mc6jfR/lsraXaeYnpZRS\nLI7bR9foKBrWinA6FKWUClo6FTAAGGP4JO4TbvjuBkIllA9Hfcjl7S7XQZVSSikOHMtgw65DDO2g\nV6uUUspJesXKz53IPMFjPz/Gtzu/ZWD0QJ7q/xRRVaOcDksppZSfWJqwH2PgAk2zrpRSjtKBlR9L\nOpTE3UvvZueRndxx7h1M6DKBENGLjEoppfLExqfSqFZVOjet5XQoSikV1Hz6X7qIjBSRBBFJFJEp\nHvZXFZFP7f2rRaSl276pdnmCiIywy5qLyBIRiRORrSJyp1v9x0QkRUQ22l+jfPnafMkYw7c7vmXc\ngnEcyjjEm8Pf5Jaut+igSimlVD6ns1ws37afoR0a6vRwpZRymM+uWIlIKDATGA4kA2tFZJ4x5ne3\nahOAg8aYNiIyDpgOXCUinYBxQGegKfCjiLQDsoB7jTHrRaQm8KuI/ODW5ovGmBm+ek2+tuvILubv\nmM/CpIXsPLKT7g26M2PQDBpF6vQOpZRSZ1q3M52jGVkM7aD9hFJKOc2XUwF7A4nGmCQAEZkDjAXc\nB1Zjgcfs7bnAq2J95DYWmGOMyQB2iEgi0NsYswrYA2CMOSoicUCzAm0GlLSTaSzauYiFSQvZlLYJ\ngJhGMdzY+UbGtBlDeEi4wxEqpZTyVz/GpVIlLIR+beo5HYpSSgU9Xw6smgG73B4nA30Kq2OMyRKR\nw0A9u/yXAsc2cz/QnjZ4LrDarXiSiFwPrMO6snWwYFAiMhGYCNCiRYuSvqZycTzzOLF/xbIgaQG/\n7PmFbJNN+zrtubvn3YxqNYrGkY0diUsppSorERkJvAyEAm8bY54psL8q8CHQEzgAXGWM2Wnvm4o1\nwyIbuMMYs6ioNkWkFTAHqAusB64zxpx2e67Lgc+BXsaYdaV9TcYYFsfv4/yz61G9ii6ZVkopp/ny\nndjTZG/jZZ0ijxWRGsAXwF3GmCN28evAE3a9J4DngZvOaMSYWcAsgJiYmILx+ExmdiYrd69kQdIC\nlu5ayqnsUzSNbMr4c8YzutVo2tRpU1GhKKVUUPHR1HSKaHM61tT0OSLyht3263YsNYE7yP+hYKkk\npR3nzwMnuLl/q7I2pZRSqhz4cmCVDDR3exwN7C6kTrKIhAFRQHpRx4pIONag6mNjzJc5FYwx+3K2\nReQtYH65vZJSchkXG1M3siBpAYv+XMThjMPUrlqbsW3GMrr1aLo36K6LjZVSyvfKfWq6Xe+MNu0p\n6kOBa+w6H9jtvm4/fgJ4Fphc1hcVG5cKwBC9f5VSSvkFXw6s1gJt7SkRKVif+F1ToM484AZgFXA5\nEGuMMSIyD/hERF7A+oSwLbDG7uTeAeKMMS+4NyQiTYwxe+yHlwBbfPS6ivXHwT9YkLSAb3d8y+7j\nu4kIjWBIiyFc3Ppi+jbtq+umlFKqYvlqarqnNusBh4wxWQXri8i5QHNjzHwRKXRg5e2U9cXx++jQ\nuCbRdaoXWkcppVTF8dnAyu6YJgGLsOafv2uM2Soi04B1xph5WIOkj+xPANOxBl/Y9T7D+jQxC7jN\nGJMtIv2B64DNIrLRfqoHjTELgWdFpDvWVMCdwN999do82XNsDwt3LGThjoVsO7iNUAmlb9O+TDp3\nEsNaDKN6uHZ8SinlEF9MTfd0/4tC64tICPAicGPhYdqVvZiyfvhkJmt3HuQfg1oX15xSSqkK4tPV\nrvaAZ2GBskfctk8BVxRy7JPAkwXKVuC508IYc11Z4y2pwxmH+f7P71mQtIBf9/0KQNcGXZnaeyoj\nWo6gXjXN0qSUUn7AJ1PTCylPA2qLSJh91SqnvCZwDrDUngLeGJgnImNKk8Bi+bb9ZLuMpllXSik/\nommESuhU1imWJi9lQdICVqSsIMuVRauoVkzqPolRrUfRvGbz4htRSilVkcp9ajrWh3xntGkfs8Ru\nY47d5tfGmMNA/ZwnE5GlwOTSZgWMjU+lbmQVujevXZrDlVJK+YAOrLyQ5cpizZ41LNixgMV/LeZ4\n5nEaVmvItR2uZVTrUXSs21GTUCillJ/yxdR0AE9t2k/5ADBHRP4NbLDbLjdZ2S6WJKQytENDQkO0\n71FKKX+hA6tCGGPYkraFhTsW8u2Obzlw6gA1w2ty4VkXMrr1aGIaxRAaEup0mEoppbxQ3lPTC2vT\nLk8iL3NgYfEM9iZuTzbsOsShE5kM02mASinlV3RgVcCfR/5kQdICFu5YyJ9H/iQ8JJxB0YMY3Xo0\nA6IHUDW0qtMhKqWUCmKL41IJCxEGtKtffGWllFIVRgdWQNrJNL7d8S0Lkhaw9cBWBKF3495MOGcC\nw84aRq0qtZwOUSmllAIgNn4fvVvVpVaE3rpDKaX8SVAPrA5lHGLi9xNZvXc1LuOiY92OTI6ZzMiW\nI2kUqVMslFJK+Zdd6SfYtu8YV/Uq/P5WSimlnBHUA6uUYynsOrqLm7vczOhWo2ldW+8HopRSyn/F\nxqcCMKxDQ4cjUUopVVBQD6xaRbVi4aULNaOfUkqpgLA4PpXWDSJpWT/S6VCUUkoV4OnO8UGjelh1\nHVQppZQKCMczsvhl+wG9WqWUUn4qqAdWSimlVKBYkZjG6WwXQzXNulJK+SUdWCmllFIBYHHcPmpG\nhBHTso7ToSillPJAB1ZKKaWUn3O5DLHx+xnUrgHhodp1K6WUP9J3Z6WUUsrPbU45TNqxDIZ11PVV\nSinlr3RgpZRSSvm5xfGphAgMbqcDK6WU8lc6sFJKKaX8XGz8PnqeVYc6kVWcDkUppVQhdGCllFJK\n+bG9h0+xJeWIZgNUSik/pwMrpZRSyo8tSUgF0PVVSinl53RgpZRSSvmxxXGpRNepRtuGNZwORSml\nVBF0YKWUUkr5KWNgReJ+hnVoiIg4HY5SSqkihDkdgFJKKaU8O5aRRUami6EddX2VUkr5O71ipZRS\nSvmpI6cyqV4llD6t6jodilJKqWL4dGAlIiNFJEFEEkVkiof9VUXkU3v/ahFp6bZvql2eICIjimtT\nRFrZbfxht6k5aZVSSgW0o6eyGNC2PhHhoU6HopRSqhg+mwooIqHATGA4kAysFZF5xpjf3apNAA4a\nY9qIyDhgOnCViHQCxgGdgabAjyLSzj6msDanAy8aY+aIyBt2268XGaTJhpOHAGNNZDfG3nYVu21c\nLlzGkO1yYVzZ9neDy+XC5XKR7XKBsb7nlBmXwWVcuFzZuIxVF5cLl8uQbax2jMEuzy5wQj0/cJ9y\n716l4Fx8wZzx8qWwNgt9Wg91JK9cCAEEETAiubVE3I/NqwMCIVa9nBasx9h1co4XDHZ7kvfaBLGf\nB0RC8h0D2D8ryP35AsY+D7nnI+fnaex6BY9zq1NwnzEF28HtOFNIOzklYn+R+9oKPkbE+rW0v2O/\n3pwyl5Hc85rTHrlt2GXGPib3VVtliODCeDhO7HBN7rkyxri9FLcyD+fZuO3P223cquVsu87Yj12W\n73S7tZv3fFjnJrctt9dnwIjbTyHnvOUdWKCu2M8vbvXt57X3GfJ+J93bdxnJq1vw70fcfqvtXSLi\n/udib1t/C2JXzH2mnOOFAse4lVGgvn1MvveEnDbF/hTNuBDjAgxiXAgu6zfAWO9XgvUeF2KyrTOS\nW9+FGGPVdz8+d9vkO16MCxFXgfICbdjbuP0uqDNlZrsYpmnWlVIqIPhyjVVvINEYkwQgInOAsYD7\nwGos8Ji9PRd4Vaz/jMcCc4wxGcAOEUm028NTmyISBwwFrrHrfGC3W/TAas8mmH5WqV6cAKH2l1JK\nKeUrgzs0cDoEpZRSXvDlwKoZsMvtcTLQp7A6xpgsETkM1LPLfylwbDN721Ob9YBDxpgsD/XzEZGJ\nwESAFk3q82WDW6xPikWsqx4SYm2H5Dy2vktIiP1psVjbEkKIiFXfrhsSEpLbVoiE5paLXSckRBAJ\ntfbbbeRuh4QQIiGEhAjk7LNjznctxO3BmdegzlRY/cLbMZ7L89V3uwKTu2ld+8i9MuB+9SFf/dxr\nKYXsy3kGz+VFb+ddLRG3KzlA3mUEIG8GbN4+434VLd9xblcrck6AWxluV+ZyLyXYx+dehYPcK2v2\ndbbcZwjJd+3Ker3WlQeTt20MIm7XswzWY+uSmX0VgDP2Yx+H8XQ9LO/nYD0XuY+tKyfi9jrzXwEV\nOfP1Ss45zXdYiNvpkjO286505lxxzF/maTv37ObsM+5XIMXeZ59Hu667/D/dglcv3Z4m59yS9zsm\nueWS97z2c+U8d86VzLxIc0+t/TjvuYzb97wram777Ppn/K2ecQHU5Huegn/POX9nRkIA6z0OEYyE\nYNwf29vGfl8zEmpfBgvJq0veY+wvg+Rr24jktgHudQUX+evltMHjnVGe1alehYY1I5wOQymllBd8\nObASD2UFxwKF1Sms3NOasKLqn1lozCxgFkBMTIy59LanPFVTSimlHBddp5rTISillPKSL5NXJAPN\n3R5HA7sLqyMiYUAUkF7EsYWVpwG17TYKey6llFJKKaWU8glfDqzWAm3tbH1VsJJRzCtQZx5wg719\nORBrrJXk84BxdtbAVkBbYE1hbdrHLLHbwG7zax++NqWUUkoppZTK5bOpgPaaqUnAIqwcD+8aY7aK\nyDRgnTFmHvAO8JGdnCIda6CEXe8zrEQXWcBtxphsAE9t2k/5ADBHRP4NbLDbVkoppZRSSimfE/e0\nyMEmJibGrFu3zukwlFIqqInIr8aYGKfj8EfaTymllPO87ad8eoNgpZRSSimllAoGOrBSSimllFJK\nqTLSgZVSSimllFJKlZEOrJRSSimllFKqjII6eYWIHAUSnI6jlOpj3b8rEGnsztDYnRGosVdk3GcZ\nYxpU0HMFFO2nHKOxO0Njd4bGXjyv+imfpVsPEAmBmolKRNZp7BVPY3eGxl7xAjXuSkj7KQdo7M7Q\n2J2hsZcfnQqolFJKKaWUUmWkAyullFJKKaWUKqNgH1jNcjqAMtDYnaGxO0Njr3iBGndlE8g/B43d\nGRq7MzR2Z/hV7EGdvEIppZRSSimlykOwX7FSSimllFJKqTLTgZVSSimllFJKlVHQDqxEZKSIJIhI\noohM8YN4movIEhGJE5GtInKnXV5XRH4QkT/s73XschGRV+z4N4lID7e2brDr/yEiN1TgawgVkQ0i\nMt9+3EpEVttxfCoiVezyqvbjRHt/S7c2ptrlCSIyooLiri0ic0Uk3j7/fQPlvIvI3fbvyxYRmS0i\nEf563kXkXRFJFZEtbmXldp5FpKeIbLaPeUVExMexP2f/zmwSka9EpLbbPo/ns7D3ncJ+Zr6K3W3f\nZBExIlLffuxX5z3YFfb74mA82k+h/VQpYtd+Kq9c+ykvY3fbF1j9lDEm6L6AUGA70BqoAvwGdHI4\npiZAD3u7JrAN6AQ8C0yxy6cA0+3tUcC3gADnAavt8rpAkv29jr1dp4Jewz3AJ8B8+/FnwDh7+w3g\nn/b2rcAb9vY44FN7u5P9s6gKtLJ/RqEVEPcHwM32dhWgdiCcd6AZsAOo5na+b/TX8w4MBHoAW9zK\nyu08A2uAvvYx3wIX+Tj2C4Ewe3u6W+wezydFvO8U9jPzVex2eXNgEfAnUN8fz3swfxX1++JgTNpP\naT9V0ri1n9J+qlSx2+UB10/59I3AX7/sk7vI7fFUYKrTcRWI8WtgOJAANLHLmmDdLBLgTeBqt/oJ\n9v6rgTfdyvPV82G80cBiYCgw3/7lTXP7g8495/YfSV97O8yuJwV/Du71fBh3Law3fSlQ7vfnHavD\n2mW/iYTZ532EP593oCX53/TL5Tzb++LdyvPV80XsBfZdAnxsb3s8nxTyvlPU34ovYwfmAt2AneR1\nWH533oP1q7DfF6fjKhCj9lPaTxUXu/ZT2k+VOnYCsJ8K1qmAOX/oOZLtMr9gX/o+F1gNNDLG7AGw\nvze0qxX2Gpx6bS8B9wMu+3E94JAxJstDHLkx2vsP2/WdiL01sB94T6zpIW+LSCQBcN6NMSnADOAv\nYA/WefyVwDjvOcrrPDeztwuWV5SbsD4Fg5LHXtTfik+IyBggxRjzW4FdgXbeKzPtp8qf9lPaT5WG\n9lPaT3ktWAdWnuZWmgqPwgMRqQF8AdxljDlSVFUPZaaIcp8RkYuBVGPMr+7FRcThN7FjfSLWA3jd\nGHMucBzrUn9h/CZ2e573WKzL+E2BSOCiIuLwm9i9UNJYHXsNIvIQkAV8nFNUSCx+EbuIVAceAh7x\ntLuQWPwi9iDjt+dW+6lCj/EV7af88+8hYN4vtZ/yWO4TwTqwSsaat5kjGtjtUCy5RCQcq7P62Bjz\npV28T0Sa2PubAKl2eWGvwYnX1g8YIyI7gTlY0yxeAmqLSJiHOHJjtPdHAekOxZ4MJBtjVtuP52J1\nYIFw3i8Adhhj9htjMoEvgfMJjPOeo7zOc7K9XbDcp+zFsRcD1xp7jkExMXoqT6Pwn5kvnI31T85v\n9t9sNLBeRBqXInZHznuQ0H6qfGk/pf1UaWk/pf2U93w1x9Cfv7A+/UnC+qHlLM7r7HBMAnwIvFSg\n/DnyL5p81t4eTf7Fe2vs8rpYc7Hr2F87gLoV+DoGk7co+HPyL3S81d6+jfyLUz+ztzuTfzFlEhWz\nKPgnoL2wgn5DAAAFbklEQVS9/Zh9zv3+vAN9gK1AdTueD4Db/fm8c+bc9XI7z8Bau27O4tRRPo59\nJPA70KBAPY/nkyLedwr7mfkq9gL7dpI3d93vznuwfhX1++JgTNpPaT9V0ri1n9J+qlSxF9i3kwDp\np3z2x+TvX1hZRbZhZT95yA/i6Y91aXITsNH+GoU1r3Ux8If9PeeXRICZdvybgRi3tm4CEu2v8RX8\nOgaT12G1xsrEkmj/QVa1yyPsx4n2/tZuxz9kv6YEKii7GNAdWGef+//Zf5ABcd6Bx4F4YAvwkf0m\n6ZfnHZiNNcc+E+sTpAnleZ6BGPs8bAdepcBCbx/Enog1nzvn7/WN4s4nhbzvFPYz81XsBfbvJK/D\n8qvzHuxfhf2+OBiP9lNG+6lSxK79VF659lNexl5g/04CpJ8S+wmVUkoppZRSSpVSsK6xUkoppZRS\nSqlyowMrpZRSSimllCojHVgppZRSSimlVBnpwEoppZRSSimlykgHVkoppZRSSilVRjqwUsoDETEi\n8rzb48ki8piDIRVKRJ4Tka0i8pyP2n/QF+0qpZQqG+2r8rWvfZVynKZbV8oDETmFdU+FXsaYNBGZ\nDNQwxjxWQc8fZozJ8rLuEayb/2X4KJZjxpgaJagvWO8tLl/Eo5RSyqJ9Vb72ta9SjtMrVkp5lgXM\nAu4uuENE3heRy90eH7O/DxaRZSLymYhsE5FnRORaEVkjIptF5Gy7XgMR+UJE1tpf/ezyx0Rkloh8\nD3xY4DnF/rRvi93WVXb5PCASWJ1TZpeHiMhOEantVpYoIo2KeP4aIvKe3f4mEblMRJ4BqonIRhH5\n2K53jx3HFhG5yy5rKSJxIvIasB5obp+nnHjPOI9KKaXKTPsq7auUHwlzOgCl/NhMYJOIPFuCY7oB\nHYF0IAl42xjTW0TuBG4H7gJeBl40xqwQkRbAIvsYgJ5Af2PMyQLtXgp0t9uvD6wVkeXGmDH2p3Td\n3SsbY1wi8jVwCfCeiPQBdhpj9onIJ4U8/8PAYWNMFwARqWOM+UJEJuW0LyI9gfFAH6y7n68WkWXA\nQaA91p3Ob7XrNTPGnGMfVxullFK+oH2V9lXKT+jASqlCGGOOiMiHwB1Awc6jMGuNMXsARGQ78L1d\nvhkYYm9fAHQSkZxjaolITXt7noeOCqA/MNsYkw3sszuIXsC8ImL5FHgEeA8YZz8u6vkvsOsBYIw5\nWEgcXxljjtuv8UtggB3Hn8aYX+x6SUBrEfkPsMDtPCillCpH2ldpX6X8hw6slCraS1jTBd5zK8vC\nnkYr1jt+Fbd97nPHXW6PXeT9vYUAfQt2SnbncbyQOKSQ8qKsAtqISAPg/wH/Lub5hf/fzv3qxBFF\nARj/ThsMVSR1fQgaggaJBNWaKjBNSpAkeCw8ABgMApJmPYI0i2IFfyqKRWKAB0AcxJ1lmw3MDkwI\niO+nZiZz555RJ2fm3AujFl3WxfEQe2beRsQkMAf8Ar4Bi88LX5LUkLmqeRzmKr0a11hJNTLzBtgH\nlv67fElpgwCYB8ae+dgDYLl/EhFfa+7t6wLfI+JjlXxmgF7dgCw703SATeAiM69HzD98faI6vIuI\n/jt2gYWIGI+IT5T2jaPhuSPiM/AhM39T2jamGryjJOkFzFWAuUrvgIWVNNoGpVe8bxuYjYgepX/7\nqS93T1kBpqtFt/+Anw3GdIC/wDlwCKxm5lWDcXvADwatFXXzrwMT1SLecwbtIFuU/v3dzDwBdiiJ\n8pjSl3/6yLxfgD8RcVbdv9YgVknSy5mrzFV6Y263LkmSJEkt+cdKkiRJklqysJIkSZKkliysJEmS\nJKklCytJkiRJasnCSpIkSZJasrCSJEmSpJYsrCRJkiSppXt2yfQMiwwE1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a095c5a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def time_nearest_neighbours_methods(item_embeddings):\n",
    "    \n",
    "    # Pairwise distances nearest neighbours\n",
    "    start = time.time()\n",
    "    distances = pairwise_distances(item_embeddings[0].reshape(1, -1), Y=item_embeddings)\n",
    "    top_items = distances.argsort()[:10]\n",
    "    end = time.time()\n",
    "    pairwise_elapsed = end - start\n",
    "    \n",
    "    #NMS lib\n",
    "    nms_idx = nmslib.init(method='hnsw', space='cosinesimil')\n",
    "    nms_idx.addDataPointBatch(item_embeddings)\n",
    "    nms_idx.createIndex(print_progress=False)\n",
    "    start = time.time()\n",
    "    nms_idx.knnQuery(item_embeddings[0])[0]\n",
    "    end = time.time()\n",
    "    nms_elapsed = end - start\n",
    "    \n",
    "    #Annoy\n",
    "    annoy_idx = AnnoyIndex(item_embeddings.shape[1])\n",
    "    for i in range(item_embeddings.shape[0]):\n",
    "        v = item_embeddings[i]\n",
    "        annoy_idx.add_item(i, v)\n",
    "    annoy_idx.build(10) # 10 trees\n",
    "    \n",
    "    start = time.time()\n",
    "    annoy_idx.get_nns_by_vector(item_embeddings[0], 10)\n",
    "    end = time.time()    \n",
    "    annoy_elapsed = end - start\n",
    "   \n",
    "    return {'pairwise_elapsed': pairwise_elapsed, 'nms_elapsed': nms_elapsed, 'annoy_elapsed' : annoy_elapsed}\n",
    "\n",
    "pairwise_timings = []\n",
    "nms_timings = []\n",
    "annoy_timings = []\n",
    "\n",
    "for i in range (1, 100, 10):\n",
    "    loop_item_embeddings = np.repeat(item_embeddings, i, axis=0)\n",
    "    results = time_nearest_neighbours_methods(loop_item_embeddings)\n",
    "    pairwise_timings.append(results['pairwise_elapsed'])\n",
    "    nms_timings.append(results['nms_elapsed'])\n",
    "    annoy_timings.append(results['annoy_elapsed'])\n",
    "    \n",
    "timings_df = pd.DataFrame({'Pairwise_dist':pairwise_timings, \\\n",
    "                           'NMS': nms_timings, \\\n",
    "                           'Annoy': annoy_timings}, \\\n",
    "                          index=np.arange(10)*item_embeddings.shape[0])\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "fig, axes = plt.subplots(nrows=1, ncols=2)\n",
    "ax = timings_df.plot(figsize=(14,4), title='Time to compute nearest neighbours vs. number of vectors', ax=axes[0])\n",
    "ax.set(xlabel='Numer of vectors', ylabel='Time (ms)')\n",
    "ax2 = timings_df.loc[:, 'Annoy':'NMS'].plot(figsize=(14,4), title='Time to compute nearest neighbours vs. number of vectors', ax=axes[1])\n",
    "ax2.set(xlabel='Numer of vectors', ylabel='Time (ms)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, both NMSLib and Annoy are a lot faster than the pairwise distance method with a larger numbers of vectors. In fact at these volumes, we can't really see any response-time increase at all as we add more vectors.\n",
    "\n",
    "## So how does using an ANN library affect quality?\n",
    "\n",
    "To get an idea, let's use our Annoy and NMS indexes to calculate predictions, and then evaluate their 'precision at K' versus the built-in predict method from LightFM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ewPyIeCAinif9LsbYhjxjgWl5eTpwgCQBHwDujYh7ACLibxHxYoVzmplZDaoEi48Du+aA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0a666f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lightfm_pak = precision_at_k(model, test, k=10).mean()\n",
    "\n",
    "def annoy_precision_at_k(user_ids, k=10):\n",
    "    test_csr = test.tocsr()\n",
    "    paks = []\n",
    "    for user_id in user_ids:\n",
    "        test_interactions = test_csr[user_id].indices\n",
    "        if len(test_interactions) > 0:\n",
    "            recommendations = annoy_member_idx.get_nns_by_vector(np.append(user_embeddings[user_id], 0), k)\n",
    "            hits = len(set(test_interactions).intersection(recommendations))\n",
    "            pak = hits / (len(test_interactions) * 1.0)\n",
    "            paks.append(pak)\n",
    "    return np.array(paks).mean()\n",
    "\n",
    "annoy_pak = annoy_precision_at_k(np.arange(test.shape[0]))\n",
    "\n",
    "def nms_precision_at_k(user_ids, k=10):\n",
    "    test_csr = test.tocsr()\n",
    "    paks = []\n",
    "    for user_id in user_ids:\n",
    "        test_interactions = test_csr[user_id].indices\n",
    "        if len(test_interactions) > 0:\n",
    "            recommendations = nms_member_idx.knnQuery(np.append(user_embeddings[user_id], 0), k=10)[0]\n",
    "            hits = len(set(test_interactions).intersection(recommendations))\n",
    "            pak = hits / (len(test_interactions) * 1.0)\n",
    "            paks.append(pak)\n",
    "    return np.array(paks).mean()\n",
    "\n",
    "nms_pak = nms_precision_at_k(np.arange(test.shape[0]))\n",
    "\n",
    "plt.bar(['LightFm', 'Annoy', 'NMSLib'], [lightfm_pak, annoy_pak, nms_pak])\n",
    "plt.title('Precision at K=10, ANN vs. exact')\n",
    "plt.ylabel('Precision at k=10')\n",
    "plt.show()"
   ]
  },
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   "source": [
    "## So, should you use one of these libraries?\n",
    "\n",
    "On a smaller dataset, it's not worth the hassle and loss of accuracy for a small increase in speed. However, if you need to respond in < 100ms, then your vector set can only grow so large before you'll need to start thinking about one of these libraries. \n",
    "\n",
    "Annoy has the advantage of saving to a memory map, and so playing well with multiple processes in a production environment\n",
    "\n",
    "NMSlib outperforms Annoy in terms of accuracy, but I also found that constructing indexes over a large dataset was slower. This becomes a problem if you have to rebuild your index frequently because of fast moving product catalogues etc. "
   ]
  }
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